I recently tried to use a non-neoprene girth on my mare instead of the neoprene that I had been using. Basically the neoprene girth was tightened a bit too tightly one day (not by me) and it rubbed a little fur off of one small area and I was afraid this would continue.
My adventure in non-neoprene was not good (see my post "If It Ain't Broke" under Horse Riding). After the saddle big time slipped and I ended up on the road, I went back to neoprene and so far its been fine. I think you just have to be really careful about how tightly you put it on. Of course some horses can have allergies too, but for the rest it's its usually fine or in my case, better.
I was normal...then I got a horse.