One way to respond is to show them why homosexuality is real (citing It’s presence in the rest of the animal kingdom, for instance), is not a mental disorder (citing presence of happy well adjusted homosexuals), etc.
Well firstly, it would be effectively impossible to show that transgender identity (stemming from gender dysphoria) is real by citing experiences among other animals - because the condition does not manifest itself in specific observed behaviours in the way that homosexuality might (although, incidentally, it's really not scientifically valid to point to (say) male lions having sexual activity with other male lions as evidence of homosexuality
per se as we would define it for humans...).
Rather, a fairly handy way of demonstrating that gender dysphoria is real and valid is simply to point to the fact that the world's mainstream expert community - people whose job it is to work this sort of stuff out, using their combined expertise and experience (expertise and experience which far, far outweighs that of, say, anyone within this thread) - now consider it to be real and valid. I don't see that as an appeal to authority at all*
And secondly, it's also scientifically questionable to say that because someone with a certain psychiatric condition is "happy (and) well-adjusted", this therefore means that the psychiatric condition is not a disorder. Very many psychopaths, for example, present as happy, well-adjusted, "normal" people (e.g. Ted Bundy as an exemplar).
I have done precisely that type of thing with people, in person, in a bi-weekly forum, for years, with regard to one aspect of my identity that makes me a minority and a markedly distasteful minority to some at times. These arguments were very heated early on, until I learned to stay calm and I understood the benefits of keeping the discussion on an even keel, because there is absolutely no chance for my interlocutor to hear me when things got heated.
Insofar as the discussion here goes, I think that perhaps the most frustrating thing (as I see it, of course) is that certain arguments are being presented
as being in support of transgender rights, while at the same effectively denying the validity of gender dysphoria (and thus seemingly approaching transgder identity as something which should be "tolerated" and "accommodated")
There is a time, perhaps, for not staying calm and for not insulting someone . I’m not aware of evidence that shows that insulting someone eventually helps to get through to them, whereas we do have evidence that rational discussion *can* - not in every case, maybe not in a majority of cases, and probably not immediately, and maybe only after a long period of time, with repeated application - help, and maybe not by itself, change minds.
I'm not sure what your definition of "insulting someone" is, within the context of this thread? Again, I have no problem with a robust attack on an argument (just as there have, er, been many such attacks on
my arguments within this very thread...). And in this specific case, there's only so many times one can ask someone here quite how, why, and on what basis of expertise/experience they are contradicting or otherwise manipulating the views of the world's experts.
* If, for example, someone argued
against the concept that electrons within atoms cannot ever be definitively isolated (for the purpose, say, of counting them), but that in fact the best one can ever do is work out the probability of any given electron being in any given place at any given time..... I'd have no philosophical trouble referring them to the collective judgement of the world's best particle physicists as a dismissal of their refutation (i.e. without having to - or needing to - get down to the granular first-order layer of proof using particle accelerators etc.