hey~ nonbinary gay here !! I'm gonna be speaking for myself but you can definitely be trans/enby and gay/lesbian, I think that cis ppl are so used to tying gender and sexuality so close to each other that sometimes they forget that those are two completely different things. so for example, if you're a man and you're only attracted to men you're gay right? but when you're nonbinary or even trans binary it's not as black and white, it's broader than that. (1)
I know that some nonbinary lesbians say that being a lesbian is their gender, and that's totally valid, just as any other group in the queer community being nonbinary and gay/lesbian is not just a this or that thing, there's a whole range of people with different believes and mindsets. From my pov the way I see it it's that I'm agender right? but my attraction towards people is gay, why? because no matter the gender (or lack of) I'm attracted to I'm always gonna be genderless, (2)
so I could be attracted to a girl and still be gay, a man? gay, any other person who isn't binary? gay. There's also the whole thing that binary people think that just because we don't fit in an woman/man gender then we HAVE to be bi or pan, when in reality that's not true, obviously that doesn't mean that bi/pan enbies aren't valid, they sure damn are, but it's once again the thing about "if you aren't this or that then your attraction can't be 'binary' either" (3)
Once again I'm talking for myself, my experience, and how I see it, this doesn't mean that every gay/lesbian nonbinary person thinks the same as me. Sorry that this got long as hell, but I hope that it helped you a bit π (4)
