I'm slightly allergic to cats (*irony*) and have had a mild reaction to Serval fur (runny nose & eyes), so I imagine there is a degree of carry-over from small to big cats (I'm not a keeper). I seem fine with lemur fur. I think in general one would only have problems if in a small area with bedding from a moulting animal (the bedding itself could potentially set me off as much as the actual animals, I think). It depends how bad the allergy is I guess - I build up some resistance from my pet cat & the nasal sprays I sometimes take in the hayfever season.
I do know a lion with hayfever, but that's another story!