Do you have to report money received from a church for providing a service (playing in the band) - in which playing an instrument is a hobby of yours anyway?

Yes. If a church is paying you for providing music during worship services or other events, you have income that should be reported on your tax return.

If the church provides a Form W-2, treat the earnings as wages from any other type of work. If you receive a Form 1099-MISC, or no form at all, your earnings should be treated as self-employment income and reported on Schedule C (Form 1040).