user-1: I'm experiencing a lot of speculative thoughts and fantasizing about the future when I'm going about my day. I'm wondering whether I should attempt to deny these thoughts, or merely let them arise without judgment. I'm also wondering whether engaging in concentrative breathing meditation will reduce this thoughts in the rest of the day, and whether the arising of these elements or other negative elements such as anger, lust, hatred, pride and narcissism can impede spiritual progress. 
I think the main question is: should one allow such thoughts non-judgmentally, even if they are delusional, or should one reduce them e.g. via the breath. The speculative and fantasy related thoughts seem to take my time, and so I wonder how one can let these thoughts arise in non-judgment without detrimental effects.

user8157: There are two methods to reduce thoughts: 
(1) Wisdom method, which is replacing unwise thoughts with wise thoughts. This will reduce the thoughts & build the wisdom that stops the re-arising of such thoughts in the future. Examples of wise thoughts are exactly what you have posted, which is thinking to yourself: "These fantasies are delusional & are a waste of time". 
(2) Concentration method, which is to use the breath to feel calmness. When the mind feels calmness, it will not be inclined to think unnecessary thoughts. 
Before the Buddha attained enlightenment, he generally used the wisdom method to reduce his unbeneficial thoughts (refer to MN 19). This is called 'yoniso manasikara' or 'wise reflection'. 
The mind is difficult to know clearly & manage therefore this is a task we each much learn. The Dhammapada states:

33. Just as a fletcher straightens an arrow shaft, even so the discerning man straightens his mind — so fickle and unsteady, so
  difficult to guard.
36. Let the discerning man guard the mind, so difficult to detect and extremely subtle, seizing whatever it desires. A guarded mind brings
  happiness.

In your situation, the wisdom method is probably the best method since you ask lots of questions here about meditation, which shows you probably need to know your mind more. 
As for 'non-judging', the Pali suttas do not really teach the practise of 'non-judging' towards unbeneficial thoughts. In addition, fantasies themselves are 'judgmments'. Therefore, if the mind was really abiding in 'non-judgment', it would not be fantasizing about the future.

user-1: {The speculative and fantasy related thoughts seem to take my time}
The reason why they do take your time is because you indulge in them.
You get carried away by these thoughts, you create more out of them.
That's what happens when we are not aware.
As soon as unbeneficial, unskillful thoughts arise, do observe them as they are. They will simply remain at the preconceptual level, they will then disappear. All of this takes place very quickly.. hence the importance of continuous mindfulness.
In reality they are merely thoughts, not you, not yours, they do not belong to anyone. They arise depending on causes and conditions.
You don't have to cling to them.
It is simply about not performing any action, not producing, not constructing.
---- The Buddha instructed thus:
"Then, Bāhiya, you should train yourself thus: In reference to the seen, there will be only the seen. In reference to the heard, only the heard. In reference to the sensed, only the sensed. In reference to the cognized, only the cognized. That is how you should train yourself. When for you there will be only the seen in reference to the seen, only the heard in reference to the heard, only the sensed in reference to the sensed, only the cognized in reference to the cognized.
Then, Bāhiya, there is no you in connection with that. When there is no you in connection with that, there is no you there. When there is no you there, you are neither here nor yonder nor between the two. This, just this, is the end of stress." - Ud 1.10 ----
http://www.accesstoinsight.org/tipitaka/kn/ud/ud.1.10.than.html
If you wish to take the samatha path, first, so that in time you will be able to use it for insight, you will need to train very diligently until the developement of the Jhanas. 
It can take many years, sooner or later you will have to practice samatha in a retreat setting as well. It is a very good way, alas quite difficult unless you renounce the lay life and meditate, day and night.
Until then, you should put emphasis on being mindful, aware, alert, here and now. "When something appears to consciousness, whatever it is, do observe and know it as it is"

-1: <p>I'm experiencing a lot of speculative thoughts and fantasizing about the future when I'm going about my day. I'm wondering whether I should attempt to deny these thoughts, or merely let them arise without judgment. I'm also wondering whether engaging in concentrative breathing meditation will reduce this thoughts in the rest of the day, and whether the arising of these elements or other negative elements such as anger, lust, hatred, pride and narcissism can impede spiritual progress. </p>

<p>I think the main question is: should one allow such thoughts non-judgmentally, even if they are delusional, or should one reduce them e.g. via the breath. The speculative and fantasy related thoughts seem to take my time, and so I wonder how one can let these thoughts arise in non-judgment without detrimental effects.</p>
 8157: <p>There are two methods to reduce thoughts: </p>

<p>(1) Wisdom method, which is replacing unwise thoughts with wise thoughts. This will reduce the thoughts &amp; build the wisdom that stops the re-arising of such thoughts in the future. Examples of wise thoughts are exactly what you have posted, which is thinking to yourself: "<em>These fantasies are delusional &amp; are a waste of time</em>". </p>

<p>(2) Concentration method, which is to use the breath to feel calmness. When the mind feels calmness, it will not be inclined to think unnecessary thoughts. </p>

<p>Before the Buddha attained enlightenment, he generally used the wisdom method to reduce his unbeneficial thoughts (refer to <a href="https://suttacentral.net/en/mn19" rel="nofollow noreferrer">MN 19</a>). This is called '<em>yoniso manasikara</em>' or 'wise reflection'. </p>

<p>The mind is difficult to know clearly &amp; manage therefore this is a task we each much learn. The Dhammapada states:</p>

<blockquote>
  <p><em>33. Just as a fletcher straightens an arrow shaft, even so the discerning man straightens his mind — so fickle and unsteady, so
  difficult to guard.</em></p>
  
  <p><em>36. Let the discerning man guard the mind, so difficult to detect and extremely subtle, seizing whatever it desires. A guarded mind brings
  happiness.</em></p>
</blockquote>

<p>In your situation, the wisdom method is probably the best method since you ask lots of questions here about meditation, which shows you probably need to know your mind more. </p>

<p>As for 'non-judging', the Pali suttas do not really teach the practise of 'non-judging' towards unbeneficial thoughts. In addition, fantasies themselves are 'judgmments'. Therefore, if the mind was really abiding in 'non-judgment', it would not be fantasizing about the future.</p>
 -1: <p>{The speculative and fantasy related thoughts seem to take my time}</p>

<p>The reason why they do take your time is because you indulge in them.
You get carried away by these thoughts, you create more out of them.
That's what happens when we are not aware.</p>

<p>As soon as unbeneficial, unskillful thoughts arise, do observe them as they are. They will simply remain at the preconceptual level, they will then disappear. All of this takes place very quickly.. hence the importance of continuous mindfulness.</p>

<p>In reality they are merely thoughts, not you, not yours, they do not belong to anyone. They arise depending on causes and conditions.
You don't <em>have</em> to cling to them.</p>

<p>It is simply about not performing any action, not producing, not constructing.</p>

<p>---- The Buddha instructed thus:</p>

<p>"Then, Bāhiya, you should train yourself thus: In reference to the seen, there will be only the seen. In reference to the heard, only the heard. In reference to the sensed, only the sensed. In reference to the cognized, only the cognized. That is how you should train yourself. When for you there will be only the seen in reference to the seen, only the heard in reference to the heard, only the sensed in reference to the sensed, only the cognized in reference to the cognized.
Then, Bāhiya, there is no you in connection with that. When there is no you in connection with that, there is no you there. When there is no you there, you are neither here nor yonder nor between the two. This, just this, is the end of stress." - Ud 1.10 ----</p>

<p><a href="http://www.accesstoinsight.org/tipitaka/kn/ud/ud.1.10.than.html" rel="nofollow noreferrer">http://www.accesstoinsight.org/tipitaka/kn/ud/ud.1.10.than.html</a></p>

<p>If you wish to take the <em>samatha</em> path, first, so that in time you will be able to use it for insight, you will need to train very diligently until the developement of the Jhanas. 
It can take many years, sooner or later you will have to practice <em>samatha</em> in a retreat setting as well. It is a very good way, alas quite difficult unless you renounce the lay life and meditate, day and night.</p>

<p>Until then, you should put emphasis on being mindful, aware, alert, here and now. "When something appears to consciousness, whatever it is, do observe and know it as it is"</p>
