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!

Many organists are not religious but appreciate the creativity and beauty of the music, buildings, and the mad range of incredibly different instruments that are all collectively called organs. Heck, in England, I've often wondered how really religious some of the clergy are...

You may find a good fit at a UU church.

An acquaintance made some money as cantor to a synagogue around here. He was not Jewish, but I gather that the combination of singing and getting paid felt just fine.