"How is one accepted as innate identity and not the other?"
As regards homosexuality, we have the interesting case that I remember from the 80s-90s where the safer sex campaigners realised that there were men out there who had sex with other men, BUT who didn't 'identify' as gay (whatever that meant, but I think more in terms of the whole social scene and 'acting' like a particular type of gay man.). Hence a separation of the objective 'who you seek to have sex with' bit, and then the 'who do you feel like inside' identity stuff. It wasn't really an issue, just that groups realised they had to be careful about their wording in material, else the men who had sex with other men but didn't identify as gay would think it wasn't aimed at them..............
As regards 'innate' and homosexuality, first I think the 'I was born this way, I can't help it scenario', was a tremendous cop-out, even if it did enable gay marriage and decriminalisation. I would have preferred, ......innate, a choice, who cares! What is it to you even if I did chose this? In fact, if I mythically had a choice, I would still chose being a lesbian!.............
Indeed, why most people are heterosexual, and exactly how they all get trained into being that way, and the social construction of sexuality, are interesting areas of study. There is no straightforward 'gay gene', even though it seems to be impossible (as well as distinctly unethical) to try and change someones sexual orientation.
I guess for me the whole difference is that 'sexual orientation' is, kind if by definition, focused outwards onto other people. It's not a case of 'I feel like a lesbian' inside, but I either fancy other women (as opposed to men), or I don't. Many women anyway have found that their sexuality is more fluid, with many women being married etc for many years before falling in love with a woman. You can feel like all the other women around you, you might not identify as anything 'different', but fancy women as opposed to men.
It's objective, rather than the magic, purely subjective 'I feel like a woman in my head' of supposed gender identity. Some women do, some women don't, and seems some males do as well. Only becomes a problem if you insist that women are supposed to 'feel like women' in the head, and that that means something significant (or means something signifcant if they don't!).