I mean, if people can self-identify their gender whatever they wish, they can also self-identify their sexuality however they wish.
But it's not a matter of self-identifying as they wish - which implies a free choice. It's self-identifying what they are - i.e. not necessarily what other people think they are.
Of course, however, no one can judge who a person
is except for that person themselves. Therefore, you are acceding to the self-identification that they desire, rather than what you (or society) might impose upon them.
I mean, I remember years back when my daughter (who is now 11) first heard about trans people. She asked me how to tell if someone was male or female. I paused, thought about it for a bit, and said you had to take their word for it.
Though I'd say fundamentally speaking I just don't hold truck with the essentialist ideas of gender, either in terms of bodies or brains. I mean, there used to be a lot of discussion of a "female brain in a male body" and vice versa, but it's kinda a problematic way to word things because it implies that brains have concrete genders, and leaves out genderqueer/agender people and the such. Much like the "born this way" defense of gayness was conservative because it acted like something was wrong with being gay, and it wouldn't be acceptable if gayness was indeed a choice.
Ultimately, it doesn't matter whether gender identity or sexuality is immutable or somewhat flexible. Peoples professed identities should be accepted at face value.