I play church gigs. The ability to play any song in any key is a big part of what makes me good at what I do.
Year ago, earlier in my development, One weekend I had a gig at a church that didn't always get the keys right in Planning Center (churches communicate with those of us involved in a service with this software). So, I had a chord chart in one key, and an mp3 in another. Rather than fight with the guy about what key it was in, I decided to take the high road and learn it (everything is memorized in my world, regardless of how little time you have to do it in) in both keys - not a big deal. I got to the church, and surprise! we were doing it in a 3rd key - this was for Saturday evening's service. That went fine, we came in on Sunday morning, and had a different singer - the worship pastor had to be at another campus, so that was what we had. The new singer says "sorry guys, my throat is trashed...could we...?" You guessed it, 4th key.
Singers are (at least in my world) the people that connect with the audience. As cool as us folks in the back may be, we're the audio equivalent of the background on the Mona Lisa - we're part of what's happening, but we don't get noticed. A good singer in the right key is far better than a great one struggling any day - part of what we do is make sure the singer is comfortable, It's just how things are. If I want to be part of a great musical experience, me struggling a bit with a tough key while the singer is comfortable is fine; the other way 'round is a train wreck. It's just part of the gig - if you sign up for it, that's what you do - flexibility is a big part of the job description.
If you have a band where a singer picks a different key, but after that, can stay with it, consider yourself lucky. I wouldn't complain about that situation at all.