Well I currently show Millie at exemption shows and she has been coming home with BPiS
Her first open show is on 21st Sept - so fingers crossed that it wouldn't affect her results there.
Basically I don't think that the white third eyelid is a deformity and hence prevent showing, it is just a cosmetic thing ... pigmented eyelids look better - as Jane Said further up.
I think though that perhaps in the case of open shows / champ shows the presence of a white 3rd eyelid may be "off-putting" to some judges, i.e if they had to choose between two identical dogs and one had a white 3rd eyelid, they may possibly choose the dog without white eyelid... just my opinion on it though :-