"But homosexuality and religion are based on feelings ...."
Except if you try to claim one or the other when applying for asylum etc, you have to provide some proof, that your claim is serious. So, claiming to be a muslim, say, whilst knowing nothing about the koran, and still attending the local baptist church every sunday, and planning to get married there next week, might be seen as not totally consistent. Similarly, if someone claimed to be a lesbian, but was currently dating and sleeping with a male, you might wonder. The facts of someone homosexuality, BTW, could be established, by testing what someone was or wasn't sexually aroused by (as too many gay men know to their cost when the standard treatment was show them pictures of naked men and give them electric shocks when they get aroused).
But this isn't really the point, as long as you allow religious groups to restrict entry to places of worship as they see fit (you can't come in, you worship next door with the baptists, we've seen you!), or allow groups to say 'sorry, you can't bring you boyfriend with you to the lesbian social'. If someone wants to call themselves a lesbian or a muslim, when others consider by their behaviour they do not qualify, that is fine. We are not required to believe whatever someone else says about themselves, when their actions contradict what they say. We are allowed to have our own opinion!
Yet when someones biology contradicts what someone says, we are supposedly not allowed to disagree. And surely the grounds for making distinctions in the latter case is stronger than just behaviour, especially given that it is actually rather important to keep stating that womanhood is not defined by what you wear, how you act etc, but by your biology.
There is no secret 'essence of lesbian', it's just you fancy women and not men, simples. Yet there is supposedly some secret 'essence of woman'...........