I don't know about a GSP, but a GWP (or Pointing Lab) or other Versatile Dog can handle both fur and feathers without a problem.

PROBABLY the reason your breeder doesn't like the idea is because when you're out hunting birds and a rabbit takes off, and your dog goes into chase mode, and thus 'accidentally' flushes lots of birds -- well, you get the picture. Also some folks think that when a pointing dog chases rabbits that it may 'ruin' their point.

AS I said, I don't know about GSPs, but both rabbits and birds are fine with a Versatile Dog (including the PL).