You need to keep the same speed ratings on them but as long as the fronts are the same and the rears are the same, it shouldn't matter much.

Racecars typically use 2 different sets of tires either the front/rears are 2 different sets or left/right are 2 different sets. It depends on the race. As long as the same type of tire are in the front or rear (basically to have the same traction and tread pattern) then it shouldn't be a problem. I had Potenzas on my fronts and Michelins on my rears on my Honda when I had to replace 2 of the tires. No need to replace all 4 when I still had 2 good tires.

I wouldn't advise having 2 different tires for the front driver/passenger or rear driver/passenger.