Q:

What makes a religion genuine or acceptable?

Often people take it for granted that we should allow people to believe whatever they believe and not critisise that they choose to be religious.
What I am wondering is what makes a belief acceptable as a religion? A person not brought up in the modern world might see Santa Claus (here meaning the idea of a fat bearded man bringing every child in the world presents on the same day) and things like Adam living 900 years as equally ridiculous (or any other story integral to some religion). It would however never be acceptable to talk about Jesus in the same way as Santa Claus.
So I am asking what separates a belief from a religion and allows it to be seen as true for some people. I'm hoping for a little more than "A lot of adults believe it so it's OK". Perhaps I can start you off with some thoughts I have had:

Why are some ancient religions that explain the origin of the earth
(Viking, Roman for example) not acceptable as religions anymore?
Could I come up with my own creation story (and make sure that it adheres
completely to modern science), and have it accepted as a religion? I would like to emphasise that it is possible to make my own religion which agrees much more closely with scientific observations than (any) other religion.

Note: I hope this is the right place to ask this question, please refer me to another SE if it is not.

EDIT: I want to point out that I can see the difference between a belief and a religion, but I cannot see a why other than many people think so.

EDIT: I know I said I would like to hear more than "A lot of adults believe it so it's OK", this does not mean I do not think it is a valid answer

A:

I'm looking for a little more than "A lot of adults believe it so it's OK".

In other words, you are not willing to accept the premise that it is nothing but because "a lot of adults believe it so".  But what if that is the correct answer, and anything else would just be a contrivance?  My conclusion is in fact a little more nuanced but this is a good starting point.
I notice currently in the wikipedia article on religion, the first sentence is annotated and I'll reproduce it here:

While religion is difficult to define, one standard model of religion, used in religious studies courses, was proposed by Clifford Geertz, who simply called it a "cultural system" (Clifford Geertz, Religion as a Cultural System, 1973).

(Emphasis mine.) I've never read Geertz, and I presume that if you actually take religious studies at a university "What is religion?" may be a controversy worthy of entire courses, graduate theses, etc.  However, I'm also going to presume that this definition, a "cultural system" is good enough, noting this does not mean that all cultural systems are religions.
One perspective on what a "cultural system" might be is indeed something "a lot of adults believe so it's OK".  That is at least a necessary property of one.  It might seem cynical to then say it is a sufficient property, but there might be a worse kind of cynicism involved in extending it further (the kind that regards culture as a means to an end).
When we talk about the value of tradition it is exactly this kind of thing we are talking about (something "a lot of adults believe so it is OK") with the qualification that "the adults" here are people we know and trust, such as our parents, their parents, etc.  I.e., we are putting our faith in something, perhaps in cases where we are uncertain of our own capacity to reason (or because it is reasonable enough to trust the trustworthy sometimes).
It is important to observe that for religious people, the significance of their religion does not seem to come from it being validated categorically as a culture.  It comes from it being the truth.  For example, what validates Christianity for a Christian is not, I think, that it satisfies a definition of religion, or that it is a coherent "cultural system", but because it is the word of God.
However, to the extent that religious people have tolerance and respect for the religion of other people it is very much about their evaluation of those religions as cultural systems.
Scientology and the controversies that surround it in the United States may be an interesting case in point.  Is Scientology a religion?  Why or why not?  I would say religious people who want to deny Scientology such status do so because they either

Are the "worse kind of cynics" I mentioned earlier, wherein culture is ultimately a means to an end (of their own particular religious vision); they probably show a varying level of intolerance toward other religions as well.

Do not want their own religiosity associated with or compared to Scientology.  These people are sort of #1 in disguise (and will tend to invoke a similar-but-softer cynical/political form of reasoning).

But what makes a religion genuine or acceptable from a secular perspective?
Simply that some group of adults profess to regard it as their own, as such (i.e., they explicitly say, "This is our religion").  As a philosopher, I'd go one step further and say it must also involve metaphysics ("What is metaphysics?" being another question).1 That's two straightforward defining characteristics. So this would be a very open definition of religion, pretty close to the one answer you've perhaps said is not good enough.
"Group" there is part of the definition.  The esoteric beliefs of an individual, metaphysical or otherwise, cannot constitute a religion until they convince others to hold them -- which is how a lot of religions explicitly got their start.
Of course, it may often be important for pragmatic purposes, under the law, to define religion in a more strict way. For example, simply on the basis of the size of the group, or, as I think is often the case, on the basis of a decision made by a government appointed board that presumably includes experts in the field of religious studies and prominent members of prominent religions (Bishops, Rabbis, etc).
However, those pragmatic purposes are not philosophical.  They are to account for people who may abuse an existing legal situation, e.g., to form a religion for tax purposes, to get more days off from work, etc.
There's also pragmatic considerations such as, "Does the religion preach violence toward others?".  But I don't think this is what you meant by (un)acceptable in your question, i.e., you could have something which is acceptable by a given definition of religion that is still not an acceptable institution socially.  I do not think we can define religion politely and say, e.g., that the Spanish Inquisition doesn't count as part of the history of the Catholic Church because "those people weren't really religious".  See #2 WRT Scientology.

1. Ruling out essentially figurative uses such as, "Guns and tequila are my religion!", although someone might come up with a coherent metaphysical order to justify that (in which case all they'd need would be adherents and presto, religion).  There might also be people who'd claim there are some non-metaphysical Eastern religions but I'll hedge that as very dubious.

A:

Let me propose as a working definition of religion, that it is a set of rituals, practices and beliefs organized around a "legitimate" attempt to understand the assumed deeper metaphysical realities of the world.  NOTE: This definition does not require you to accept that there ARE deeper metaphysical realities, only that there exist legitimate attempts to understand them. 
So what would constitute "legitimate" under this understanding?  "Santa Claus" would not count, because he is understood to be a fairy tale told to children.  He is not generally understood by any adult to be representing any deeper reality.  The Flying Spaghetti Monster doesn't count, it is a parody of religion with the distinctive trait that it is not believed by any of its adherents.  Norse religion is not currently accepted as a legitimate belief system by any significant number of adherents, so while it might have been a legitimate religion at one time, it cannot be considered one now. Scientology is an edge case, because it is widely believed to have been deliberately invented, without any true belief by its founder, yet is arguably legitimately believed by its adherents.  
In contrast to the above, religions like Christianity, Islam, Taoism and Hinduism may hold incompatible beliefs, but they can all be considered "legitimate" attempts to understand God and the universe, whether or not you endorse one and reject the others, or even whether you personally believe God exists.

A:

What I am wondering is what makes a belief acceptable as a religion?

Religion is more of a system of beliefs, not just a single belief. 
Clearly belief that "Justin Bieber sucks" doesn't constitute religious belief, but belief that "the Buddha is a good example to follow" or "That God was the cause of the Big Bang" does. Although there can be no formal rule for what constitutes religious belief and what doesn't, Wittgenstein's concept of family resemblance can help us. We have set of prototypes and examples of what a member of that category looks like, and based on that we can determine whether a new instance belongs into that category or not. Obviously, this leads to fuzzy boundaries, and it becomes questionable whether some things fall in the category of religion or not (e.g. Confucianism), but the central prototypes do remain clear. For example, anything with a cosmology and a set of dos and don's based on that cosmology is undisputedly a religion.  

Why are some ancient religions that explain the origin of the earth (Viking, Roman for example) not acceptable as religions anymore?

One answer is sheer demographics. The examples you mentioned simply disappeared the same way Amerindians disappeared from North America, or Europeans switched from drinking mead to drinking beer and wine. 
There is a second point of view (I need to go back and search for the sources): There is an evolution from polytheism to monotheism, since monotheism represents a more "advanced" belief system than polytheism. Advocates of this world view point to Plato dismissing the Greek gods and moving towards his concept of the one, the evolution of Hinduism from being polytheistic in the Vedas to clearly monotheistic in the Bhagavad Gita, and the evolution of semitic religions from the various Canaanite and Babylonian gods to Abrahamic monotheism. In this context, it was inevitable that people would move away from Roman and Nordic gods, since those represent primitive beliefs compared to the current ones Europe holds. 
One variation on this point of view (again I need to look for the source), is that after polytheism and then monotheism, the next stage is belief in science and in abstract principles, which leads to your next question: 

Could I come up with my own creation story [...], and have it accepted as a religion? 

You could. L. Ron Hubbard supposedly decided that the best way to get rich was to invent a new religion, and that's why he came up with Scientology. He seems to have been successful, as the Church of Scientology is considered officially a religion by the US government (by the organization's tax status). 
So yes it can be done. Your challenge would be to convince people to follow you and have people with money build places of worship for you. 

(and make sure that it adheres completely to modern science), and have it accepted as a religion? I would like to emphasise that it is possible to make my own religion which agrees much more closely with scientific observations than (any) other religion.

You already have a worldview or cosmology based on science. The major challenges you are facing here: 

Can you construct a system of values and ethics (dos and don'ts, commandments, etc...) based on science? This is not obvious at all. 
If there is one common thread to all religions, it is a set of rituals. You will need to come up with a meaningful set of rituals to attract and keep your followers. 

See the following question: 
Can belief in science be considered a form of theism?

