I think you may be confused as to the purpose of tags. Tags are a method we have of finding and searching for questions and for allowing people to follow topics they are interested in. It isn't meant to pigeonhole an entire community of diverse people into one heading.
After a very brief look at questions tagged "homosexuality" I can see some evidence that what you say it true. I can also see some questions that are specifically about homosexuality (in the literal sense of being attracted to someone of the same sex, not referencing any specific community of people) and not about any LGBTQ community.
And this is where it gets tricky. Since the "homosexuality" tag doesn't have a wiki, there isn't really any guidance on how it should be used and if it is being used correctly on questions. Thus, without reading every question, I can't know whether someone is asking about same-sex attraction or referring to an LGBTQ community. And it can be hard to determine what the original author meant as well. So given this along with the (brief) research cited above, a blanket change may not be appropriate, as it might ascribe an incorrect meaning to questions the original authors never intended.
So what can we do? Well, I would suggest starting with doing some research. Right now, there are 14 questions tagged with "homosexuality". (There also may be more that aren't tagged with that, which you may want to look for.) We need to figure out which ones are talking about communities (or where such a tag would be beneficial) and which ones are strictly about same-sex attraction. If you can do that, that will go a long way to helping us pick an appropriate plan of action.
For example, if most of those questions are really about same-sex attraction, we can add that to the tag wiki, making it known that that tag is only about that and not any LGBTQ community. We also might consider renaming the tag to "same-sex attraction" or creating synonyms, etc. We could then just drop the tag on any question where it is inappropriate.
If we find enough questions that are actually talking about those communities, then maybe it makes sense to create an "LGBTQ" tag and add that where appropriate.
In either case, we may want to rename "homosexuality" to "same-sex attraction". How and when we go about this depends a lot on what your research turns up.
I'm using LGBTQ here to represent all the communities you've referenced.
I can't remember the full alphabet soup acronym for them all.