If you're in the US, you may want to try to find an episcopal church. They seem to be liturgically conservative enough to still have organs but are generally socially liberal enough to be more accepting. Ymmv, obviously.

But I will say that personally in years of playing the organ and asking random churches (including conservative ones) if I could borrow their organs on a quiet weekday, my bisexuality has never come up. And I didn't have to be friends with the choir director either. Once, I attended one Mass and just went up to him afterwards to thank him for playing (it was beautiful) and ask if I could ever practice with it.

I know it's different from many places as I'm in a big city, but at least four organists whom I've known personally are gay. Many churches don't even require you to be religious even to be employed to play the organ there. Randomly on an airplane, I spoke with an atheist music professor who was choir director/organist at a congregationalist church. They didn't seem to care. So I doubt it'd be a big deal if you just want to practice. The choir director at my current (liberal) parish never takes Communion--I don't know if he is personally religious one way or the other, but it seems to be little more than a job to him.

Also, you should try to find some churches where there is more than just "drab church hymns." 20th and even 21st century voluntaries, anthems, and choral preludes are alive and well in certain segments of Christendom. See for instance the churches that Bálint Karosi plays in. I doubt you'd describe his music as "drab." My parish runs the gamut from Palestrina to something from the 20th century at least every Sunday. Just my 2 cents.