user14827: Supposed that respect, veneration and any kind of wisdom has gone missing; and that the Sangha has become a group of householder wearing robes; and the leaders of the Sasana are all but householders. In that case, should the Noble Sangha, the Savaka Sangha, let go of their heritage, like one with Sila would give up a book that has become a target of white ants?
It's a serious question.
While the Buddha did not allow his monks to give up Sangha heritage, generally he allowed it in case thieves and robbers would destroy things and harm in cases the monks would hold on it.
Is that, the degeneration, actually the reason why such as householder movements became that popular?
Spoken in numbers, there are about 99% of laypeople (incl. those in robes) who are engaged in depriving the Dhamma from the Sangha, making a livelihood from it; and somewhat 1% who dedicate their sacrifices toward the gems, and respect the recluses.
I doubt that any at large had understood the meaning of "making the Dhamma your own", yet, with total confusion, running after it out of context.
Should the Noble Sangha let them follow their inclinations which brings not only them long time suffering but for many? Resting simply in "Beings are heirs of their kamma..." or still share as much as compassion as possible to keep those able away from doing really grave wrong doings?

user471: Firstly, you may need to choose your monastery or teacher carefully. Ajahn Brahm once said in a talk that he visited various monasteries and teachers and found that most of them were gloomy or stoic. He finally chose Ajahn Chah because Ajahn Chah and his disciples were happy and smiling, so they must be doing something right, he thought.
But if you listen to more of his talks, you will find him mentioning about abbots or senior monks who take the best food for themselves, and then mix the rest of the food together for the rest of the monks. So, there's no perfect situation with regards to the monastic order, I suppose.
Secondly, the last resort is to take the Buddha's Words (Buddhavacana) as your teacher and to take refuge in (and take example of) the ideal Sangha and not the conventional Sangha.
If you feel that you cannot trust some or all of the members of the Sangha, please use the Buddha's Words (Buddhavacana) in the suttas as your teacher, as it is said in the Mahaparinibbana Sutta: 

Now, if it occurs to any of you — 'The teaching has lost its
  authority; we are without a Teacher' — do not view it in that way.
  Whatever Dhamma & Vinaya I have pointed out & formulated for you, that
  will be your Teacher when I am gone.

From Thanissaro Bhikkhu's essay on Refuge, we understand that we should differentiate the conventional Sangha from the ideal Sangha, and use the ideal Sangha as our example (since "not all members of the conventional Sangha are reliable models of behavior"):

The word Sangha, on the external level, has two senses: conventional
  and ideal. In its ideal sense, the Sangha consists of all people, lay
  or ordained, who have practiced the Dhamma to the point of gaining at
  least a glimpse of the Deathless. In a conventional sense, Sangha
  denotes the communities of ordained monks and nuns. The two meanings
  overlap but are not necessarily identical. Some members of the ideal
  Sangha are not ordained; some monks and nuns have yet to touch the
  Deathless. All those who take refuge in the Buddha, Dhamma, and Sangha
  become members of the Buddha's four-fold assembly (parisa) of
  followers: monks, nuns, male lay devotees, and female lay devotees.
  Although there's a widespread belief that all Buddhist followers are
  members of the Sangha, this is not the case. Only those who are
  ordained are members of the conventional Sangha; only those who have
  glimpsed the Deathless are members of the ideal Sangha. Nevertheless,
  any followers who don't belong to the Sangha in either sense of the
  word still count as genuine Buddhists in that they are members of the
  Buddha's parisa.
When taking refuge in the external Sangha, one takes refuge in both
  senses of the Sangha, but the two senses provide different levels of
  refuge. The conventional Sangha has helped keep the teaching alive for
  more than 2,500 years. Without them, we would never have learned what
  the Buddha taught. However, not all members of the conventional Sangha
  are reliable models of behavior. So when looking for guidance in the
  conduct of our lives, we must look to the living and recorded examples
  provided by the ideal Sangha. Without their example, we would not know
  (1) that Awakening is available to all, and not just to the Buddha;
  and (2) how Awakening expresses itself in real life.
On the internal level, the Buddha, Dhamma, and Sangha are the skillful
  qualities we develop in our own minds in imitation of our external
  models. For instance, the Buddha was a person of wisdom, purity, and
  compassion. When we develop wisdom, purity, and compassion in our own
  minds, they form our refuge on an internal level. The Buddha tasted
  Awakening by developing conviction, persistence, mindfulness,
  concentration, and discernment. When we develop these same qualities
  to the point of attaining Awakening too, that Awakening is our
  ultimate refuge. This is the point where the three aspects of the
  Triple Gem become one: beyond the reach of greed, anger, and delusion,
  and thus totally secure.

Also from the ATI Sangha page, it clarifies that the ideal Sangha is composed of those who are of the 8 types - those who are genuinely and sincerely trying to attain the four stages of enlightenment, and those that have successfully attained the four stages of enlightenment (stream entry, once-returner, never-returner and arahant):

In the suttas the word sangha (lit. "group, assembly") is usually used
  in one of two ways: it refers either to the community of ordained
  monks and nuns (bhikkhu-sangha and bhikkhuni-sangha) or to the
  community of "noble ones" (ariya-sangha) — persons who have attained
  at least stream-entry, the first stage of Awakening. The definition
  (ariya-sangha)

"The Sangha of the Blessed One's disciples who have practiced well...
    who have practiced straight-forwardly... who have practiced
    methodically... who have practiced masterfully — in other words, the
    four types [of noble disciples] when taken as pairs, the eight when
    taken as individual types — they are the Sangha of the Blessed One's
    disciples: worthy of gifts, worthy of hospitality, worthy of
    offerings, worthy of respect, the incomparable field of merit for the
    world."
— AN 11.12



user254: Although "Dhamma" is in the title, the text of the question seems to be asking instead about the Discipline:
If the Sangha has become a group of householder wearing robes, should the Noble Sangha let go of their heritage? ... 
Would the Buddha allow monks to give up Sangha heritage in that case?
I read The Broken Buddha so it's not completely new to me to hear of someone saying something like, "the leaders of the Sasana are all but householders".
I wouldn't want to say that, and I couldn't say it about anyone (because I don't know them), but I suppose that what's written in the book has some truth in it, even if only that it's as-witnessed.
Similarly I read a little of the "austere Forest Tradition" -- specifically as contrasted with the living and so on in towns.
I don't have a specific answer for you -- I think there are several:

You might want to find a monastery which you approve of -- a bikkhu, a group of bikkhus, who you approve of. People's biographies, monks and nuns too, often include their visiting and studying in several places, studying under several teachers.
It's common to disrobe -- not that I'm recommending that, but perhaps that's what you meant by "give up Sangha heritage". Perhaps some people who do that give up parts of the the Discipline, but not the Dhamma.
Perhaps consider being less critical of others -- I assume you are critical of others, "You shouldn't practice/live that way", "You don't have a proper teacher", "Your motives aren't proper", etc. To pick an example almost at random, there's this Wikipedia article about Ajahn Sumedho -- which describes him as "engaging and witty communication style", and pictures him and the monk who he's talking with laughing together. Then again the biography of Ajahn Chah says, "He sometimes initiated long and seemingly pointless work projects, in order to frustrate their attachment to tranquility" -- possibly you have some attachment to the way things ought to be, how other people ought to behave.

Is that, the degeneration, actually the reason why such as householder movements became that popular?
How popular is "that popular", what "householder movements"? Perhaps what you're talking about is an "observation bias" i.e. if you observe householder movements then that's what you see; and if you e.g. read the internet less then you wouldn't see them so much -- but I don't know what you're talking about. You see different things than I do, and perhaps you see them differently -- the all.
There are articles in the Appendix which say e.g. (in 1931) that ...

Already prominent laymen in Burma, Siam, Ceylon, and elsewhere, view with misgivings the present state of affairs and know that sooner or later some alterations will have to be made. Nearly everyone sees signs of decay in the Order, that Order that has continued for 2500 years, but today there are new conditions and forces in the world and unless something radical is done this decay will increase until either the Sangha dies out, or becomes a dead letter, the refuge of the ignorant and unworthy.

It isn't only monks of Western origin who say this. Anyway you might want to read The Broken Buddha assuming you haven't already. I think it talks about issues (i.e. problems within Sangha) which you question here, and quote various people who suggest solutions, and maybe you can find in it some people or organisations who you might concur with.
I don't know that I can answer this question, though, since I don't know what you mean by "householder movements".
I suppose that everyone (householders too) must practice on their own (as "islands"), AND that the Sangha is, has been, will be important.
Should the Noble Sangha let them follow their inclinations which brings not only them long time suffering but for many?
I don't know that it's possible to prevent people from doing what's harmful -- if you knew how to, perhaps you could help drug addicts? -- and if you can't prevent them then I don't see how it's a question of "letting them".
If someone only sees you as getting into arguments, and scolding people, etc., I suppose that's not effective.
Resting simply in "Beings are heirs of their kamma..." or still share as much as compassion as possible to keep those able away from doing really grave wrong doings?
I think the theory is that it isn't one OR the other (i.e. compassion OR equanimity) -- instead it's both (i.e. "and") -- or rather, all four (mudita and metta too).
Also you practice one whenever you can't practice another -- or perhaps one is an antidote to an excess of the other.

14827: <p>Supposed that respect, veneration and any kind of wisdom has gone missing; and that the Sangha has become a group of householder wearing robes; and the leaders of the Sasana are all but householders. In that case, should the Noble Sangha, the Savaka Sangha, let go of their heritage, like one with Sila would give up a book that has become a target of white ants?</p>

<p>It's a serious question.</p>

<p>While the Buddha did not allow his monks to give up Sangha heritage, generally he allowed it in case thieves and robbers would destroy things and harm in cases the monks would hold on it.</p>

<p>Is that, the degeneration, actually the reason why such as householder movements became that popular?</p>

<p>Spoken in numbers, there are about 99% of laypeople (incl. those in robes) who are engaged in depriving the Dhamma from the Sangha, making a livelihood from it; and somewhat 1% who dedicate their sacrifices toward the gems, and respect the recluses.</p>

<p>I doubt that any at large had understood the meaning of "making the Dhamma your own", yet, with total confusion, running after it out of context.</p>

<p>Should the Noble Sangha let them follow their inclinations which brings not only them long time suffering but for many? Resting simply in "Beings are heirs of their kamma..." or still share as much as compassion as possible to keep those able away from doing really grave wrong doings?</p>
 471: <p>Firstly, you may need to choose your monastery or teacher carefully. Ajahn Brahm once said in a talk that he visited various monasteries and teachers and found that most of them were gloomy or stoic. He finally chose Ajahn Chah because Ajahn Chah and his disciples were happy and smiling, so they must be doing something right, he thought.</p>

<p>But if you listen to more of his talks, you will find him mentioning about abbots or senior monks who take the best food for themselves, and then mix the rest of the food together for the rest of the monks. So, there's no perfect situation with regards to the monastic order, I suppose.</p>

<p>Secondly, the last resort is to take the Buddha's Words (Buddhavacana) as your teacher and to take refuge in (and take example of) the ideal Sangha and not the conventional Sangha.</p>

<p>If you feel that you cannot trust some or all of the members of the Sangha, please use the Buddha's Words (Buddhavacana) in the suttas as your teacher, as it is said in the <a href="https://www.accesstoinsight.org/tipitaka/dn/dn.16.5-6.than.html" rel="nofollow noreferrer">Mahaparinibbana Sutta</a>: </p>

<blockquote>
  <p>Now, if it occurs to any of you — 'The teaching has lost its
  authority; we are without a Teacher' — do not view it in that way.
  Whatever Dhamma &amp; Vinaya I have pointed out &amp; formulated for you, that
  will be your Teacher when I am gone.</p>
</blockquote>

<p>From Thanissaro Bhikkhu's essay on <a href="https://www.accesstoinsight.org/lib/authors/thanissaro/refuge.html" rel="nofollow noreferrer">Refuge</a>, we understand that we should differentiate the conventional Sangha from the ideal Sangha, and use the ideal Sangha as our example (since "<em>not all members of the conventional Sangha are reliable models of behavior</em>"):</p>

<blockquote>
  <p>The word Sangha, on the external level, has two senses: conventional
  and ideal. In its ideal sense, the Sangha consists of all people, lay
  or ordained, who have practiced the Dhamma to the point of gaining at
  least a glimpse of the Deathless. In a conventional sense, Sangha
  denotes the communities of ordained monks and nuns. The two meanings
  overlap but are not necessarily identical. Some members of the ideal
  Sangha are not ordained; some monks and nuns have yet to touch the
  Deathless. All those who take refuge in the Buddha, Dhamma, and Sangha
  become members of the Buddha's four-fold assembly (parisa) of
  followers: monks, nuns, male lay devotees, and female lay devotees.
  Although there's a widespread belief that all Buddhist followers are
  members of the Sangha, this is not the case. Only those who are
  ordained are members of the conventional Sangha; only those who have
  glimpsed the Deathless are members of the ideal Sangha. Nevertheless,
  any followers who don't belong to the Sangha in either sense of the
  word still count as genuine Buddhists in that they are members of the
  Buddha's parisa.</p>
  
  <p>When taking refuge in the external Sangha, one takes refuge in both
  senses of the Sangha, but the two senses provide different levels of
  refuge. The conventional Sangha has helped keep the teaching alive for
  more than 2,500 years. Without them, we would never have learned what
  the Buddha taught. <strong>However, not all members of the conventional Sangha
  are reliable models of behavior. So when looking for guidance in the
  conduct of our lives, we must look to the living and recorded examples
  provided by the ideal Sangha.</strong> Without their example, we would not know
  (1) that Awakening is available to all, and not just to the Buddha;
  and (2) how Awakening expresses itself in real life.</p>
  
  <p>On the internal level, the Buddha, Dhamma, and Sangha are the skillful
  qualities we develop in our own minds in imitation of our external
  models. For instance, the Buddha was a person of wisdom, purity, and
  compassion. When we develop wisdom, purity, and compassion in our own
  minds, they form our refuge on an internal level. The Buddha tasted
  Awakening by developing conviction, persistence, mindfulness,
  concentration, and discernment. When we develop these same qualities
  to the point of attaining Awakening too, that Awakening is our
  ultimate refuge. This is the point where the three aspects of the
  Triple Gem become one: beyond the reach of greed, anger, and delusion,
  and thus totally secure.</p>
</blockquote>

<p>Also from the <a href="https://www.accesstoinsight.org/ptf/sangha.html" rel="nofollow noreferrer">ATI Sangha</a> page, it clarifies that the ideal Sangha is composed of those who are of the 8 types - those who are genuinely and sincerely trying to attain the four stages of enlightenment, and those that have successfully attained the four stages of enlightenment (stream entry, once-returner, never-returner and arahant):</p>

<blockquote>
  <p>In the suttas the word sangha (lit. "group, assembly") is usually used
  in one of two ways: it refers either to the community of ordained
  monks and nuns (bhikkhu-sangha and bhikkhuni-sangha) or to the
  community of "noble ones" (ariya-sangha) — persons who have attained
  at least stream-entry, the first stage of Awakening. The definition
  (ariya-sangha)</p>
  
  <blockquote>
    <p>"The Sangha of the Blessed One's disciples who have practiced well...
    who have practiced straight-forwardly... who have practiced
    methodically... who have practiced masterfully — in other words, the
    four types [of noble disciples] when taken as pairs, the eight when
    taken as individual types — they are the Sangha of the Blessed One's
    disciples: worthy of gifts, worthy of hospitality, worthy of
    offerings, worthy of respect, the incomparable field of merit for the
    world."</p>
    
    <p>— <a href="https://www.accesstoinsight.org/tipitaka/an/an11/an11.012.than.html" rel="nofollow noreferrer">AN 11.12</a></p>
  </blockquote>
</blockquote>
 254: <p>Although "Dhamma" is in the title, the text of the question seems to be asking instead about the Discipline:</p>

<p><strong>If the Sangha has become a group of householder wearing robes, should the Noble Sangha let go of their heritage? ... 
Would the Buddha allow monks to give up Sangha heritage in that case?</strong></p>

<p>I read <em><a href="https://www.bhantedhammika.net/the-broken-buddha" rel="nofollow noreferrer">The Broken Buddha</a></em> so it's not completely new to me to hear of someone saying something like, "the leaders of the Sasana are all but householders".</p>

<p>I wouldn't want to say that, and I couldn't say it about anyone (because I don't know them), but I suppose that what's written in the book has some truth in it, even if only that it's as-witnessed.</p>

<p>Similarly I read a little of the "austere Forest Tradition" -- specifically as contrasted with the living and so on in towns.</p>

<p>I don't have a specific answer for you -- I think there are several:</p>

<ul>
<li>You might want to find a monastery which you approve of -- a bikkhu, a group of bikkhus, who you approve of. People's biographies, monks and nuns too, often include their visiting and studying in several places, studying under several teachers.</li>
<li>It's common to disrobe -- not that I'm recommending that, but perhaps that's what you meant by "give up Sangha heritage". Perhaps some people who do that give up parts of the the Discipline, but not the Dhamma.</li>
<li>Perhaps consider being less critical of others -- I assume you are critical of others, "You shouldn't practice/live that way", "You don't have a proper teacher", "Your motives aren't proper", etc. To pick an example almost at random, there's this Wikipedia article about <a href="https://en.wikipedia.org/wiki/Ajahn_Sumedho" rel="nofollow noreferrer">Ajahn Sumedho</a> -- which describes him as "engaging and witty communication style", and pictures him and the monk who he's talking with laughing together. Then again the biography of <a href="https://forestsangha.org/ajahn-chah/biography" rel="nofollow noreferrer">Ajahn Chah</a> says, "He sometimes initiated long and seemingly pointless work projects, in order to frustrate their attachment to tranquility" -- possibly you have some attachment to the way things ought to be, how other people ought to behave.</li>
</ul>

<p><strong>Is that, the degeneration, actually the reason why such as householder movements became that popular?</strong></p>

<p>How popular is "that popular", what "householder movements"? Perhaps what you're talking about is an "observation bias" i.e. if you observe householder movements then that's what you see; and if you e.g. read the internet less then you wouldn't see them so much -- but I don't know what you're talking about. You see different things than I do, and perhaps you see them differently -- the all.</p>

<p>There are articles in the <a href="https://www.bhantedhammika.net/the-broken-buddha/appendix" rel="nofollow noreferrer">Appendix</a> which say e.g. (in 1931) that ...</p>

<blockquote>
  <p>Already prominent laymen in Burma, Siam, Ceylon, and elsewhere, view with misgivings the present state of affairs and know that sooner or later some alterations will have to be made. Nearly everyone sees signs of decay in the Order, that Order that has continued for 2500 years, but today there are new conditions and forces in the world and unless something radical is done this decay will increase until either the Sangha dies out, or becomes a dead letter, the refuge of the ignorant and unworthy.</p>
</blockquote>

<p>It isn't only monks of Western origin who say this. Anyway you might want to read <em>The Broken Buddha</em> assuming you haven't already. I think it talks about issues (i.e. problems within Sangha) which you question here, and quote various people who suggest solutions, and maybe you can find in it some people or organisations who you might concur with.</p>

<p>I don't know that I can answer this question, though, since I don't know what you mean by "householder movements".</p>

<p>I suppose that everyone (householders too) must practice on their own (as "islands"), AND that the Sangha is, has been, will be important.</p>

<p><strong>Should the Noble Sangha let them follow their inclinations which brings not only them long time suffering but for many?</strong></p>

<p>I don't know that it's possible to prevent people from doing what's harmful -- if you knew how to, perhaps you could help drug addicts? -- and if you can't prevent them then I don't see how it's a question of "letting them".</p>

<p>If someone only sees you as getting into arguments, and scolding people, etc., I suppose that's not effective.</p>

<p><strong>Resting simply in "Beings are heirs of their kamma..." or still share as much as compassion as possible to keep those able away from doing really grave wrong doings?</strong></p>

<p>I think the theory is that it isn't one OR the other (i.e. compassion OR equanimity) -- instead it's both (i.e. "and") -- or rather, all four (<em>mudita</em> and <em>metta</em> too).</p>

<p>Also you practice one whenever you can't practice another -- or perhaps one is an antidote to an excess of the other.</p>
