I know 2 great pianists that can transpose while reading a music sheet in real time to any key. I become really impressed when i see them playing that way.
I can easily transpose songs I had already memorized to every natural key but I find a little harder transposing especially to D flat, and G flat. Overall I'm quite confortable with the rest.

I already played with with that kind of "beer singers" having to transpose 3 or 4 times during a song.

Sometimes it's easier if you hear the "beer singer", quickly find the close key you can play and use the tranpose function of your keyboard, of course.

If you sound bad, because the key changes of the singer, sometimes they will think you're a bad musician!!! Often the crowd thinks you have to play everything in every key. For them it's just "playing".

Luis Santos