I never know what the song list is for Sundays. However, I do know that whatever song they sing will be familiar because they don't sing anything that they haven't practiced.
The key is knowing familiar chord progressions. Even if you've never heard the song, if you can follow the progression of their voices, you can make it through just about any unfamiliar song. I've gotten to the point where I can tell when their voices is leading me to play a 2-5-1, or 7-3-6, etc.
I hear ya. Lately though, if everyone is clueless, song goes undone. Yes we have left a visiting minister singing a capella.
I've done that many times, and am not shamed about it. They better start bringing their own musicians wit em or have some music tracks.