Stop being part of one church, keep your login and any other church you play at.
Your profile → Your data → Leave <church>. There is one button per church you belong to, each named, so you can't leave the wrong one.
What happens. Your membership, your availability and your place on that church's future rotas and services are removed at once, and its admins are told you've left. Past services and the rota history are kept — a service you played in March still exists. Your login stays, and so does any other church you belong to. That church's songs, services and rota are cleared from this device.
You can be invited back at any time; it makes a new membership, not the old one.
If you're the only admin, Unison refuses and points you at the Team screen: make someone else an admin first, then leave. A church cannot be left with nobody in charge of it.
Needs a connection, and your two-step code if you have one.