What are the stipulations to wearing a hair system after FUE?

It is best to ask your surgeon about post operative care as each doctor has their unique regimen.  You can wear a hair system as long as the grafts are secure.

You may wear a hair system without any glue or adhesive tape 10 days after surgery . But I strongly disagree to use any kind of hair piece or wig that contains glue or adhesives for fixing  it to scalp because of devastating effect of chemicals to scalp and hair follicles  both implanted and preexisting ones . 

It is typically fine to wear a hair piece after a hair transplant surgery. It is crucial, though, to be aware of in which manner the hair piece is fixed on the scalp. Hair pieces of high quality are mostly manufactured in a thin skin-like material, with the hairs being woven into or even glued in place on the scalp. Typically, the hair piece is predominantly fixed on the already present hairs or onto the skin surface. It can not be fixed in the recipient zone post-op. Fixing of the hair piece can be accomplished using clips or adhesive tape on areas of the scalp in which surgery was not performed.

The use of hats after hair transplants is only limited by not rubbing against the recipient or donor area so as not to cause irritation or infection