I’m planning on starting a group fitness studio. Is having a shower a necessity?

It might affect your business a bit, but I do know of a couple of privately owned fitness studios that have bathrooms and a very small changing area, but not a shower.

I would say, at a minimum, you should have a bathroom that is large enough for people to change clothes without bumping into the toilet, or a separate changing area (much more sanitary than changing in a bathroom stall).