Indeed! I don't know if you remember, but I once wrote a story about working with voice-training tapes in high school. Precisely because I did not want to be perceived as gay.
It took me decades to let go of that and just let myself speak.
It's funny. I've spent many hours talking to you on the phone and over meeting apps, and it never occurred to me that you sound British.
If anything, you sound to me like an NPR host. Think Ira Glass, only with a lower pitched, more resonant voice. (Ira really is little nasally sounding. You are not, in my opinion .)
Accents and registers, native or acquired, communicate a lot about a us. Even when we don't intend them to.
What I think is that your manner of speaking is truly authentic. You don't sound the least bit affected. You sound exactly like you — like the same person who shines through in your writing and your other art.
Where the British question comes from, now that's a puzzler.
There are many, many accents in the U.K., far more than in North America. This is to be expected given the area of the UK is the birthplace of English, and linguists have learned that language diversity increases the closer one comes to language origin points.
Your accent doesn't resemble (to my ears) any of the hundreds of distinct accents in the British isles.
But the fact that some Americans think it does might really reflect something.
It's a fascinating topic to think about, especially when the question of accent can be wrapped up with queer identity.