Is it okay to place a propane water heater right next to my water pressure tank?
I was worried about the electrical pressure switch being too close to the gas water heater.

The heater spec will usually give you the clearances it must be from other fixtures. "Right next to" is a bit vague but I'd leave at least a 1' space. I see no danger from the switch unless your propane supply line isn't gas tight, then you will have an issue even if the switch were yards away.