My french horn teacher was a new-age "recovering Catholic"[1] and a paid singer for a couple Protestant churches. A job is a job. Personally, I am an atheist but I find a lot of devotional music to be well written and fun to sing, and I enjoy singing it in choir, even if I don't literally believe the words I'm singing.

In any event, you can play organ with a community choir, especially if you can also play piano. We pay our accompanists.

1. i.e. no longer Christian

I understand completely — doctrinal disagreement keeps me out of men’s choirs, musical theatre, and men‘s gyms, too!

You may find a good fit at a UU church.