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.