Does the FAA restrict the color of pilot seat belts?
No, there's no regulation on the color; the restraints just have to allow the crew to perform all their duties.

The old 23.785 regulation said:


  (e) The restraint system for each crewmember must allow the crewmember, when seated with the safety belt and shoulder harness fastened, to perform all functions necessary for flight operations.


The new 23.2535 regulation says even less:


  Safety and survival equipment, required by the operating rules of this chapter, must be reliable, readily accessible, easily identifiable, and clearly marked to identify its method of operation.


And empirically, there are many colors available. Googling will bring up plenty of images.