As someone who tried to attend culinary school but could not because of physical limitations, I actually don't like wearing gloves while cooking. For starters, people don't tend to think about germs and cross contamination as much when it isn't directly on their hands, so they may go from say raw chicken to something cooked without a glove change or a wash. Second, you can't pick up temps as quickly or accurately with the gloves on and I always worry about touching a very hot pan and melting the glove and getting burned. Third, you don't have the good feel when slicing and I find it easier to cut a finger.

Anyway, I agree with the others, ask your server and the manager if the kitchen staff uses latex gloves and if they do, have it noted directly on the kitchen ticket about your allergy and if the manager can watch the prep, even better. It much the same as someone with a peanut allergy will request that if peanuts are used in the prep of some food, that different cookware be used for their dishes to avoid any peanut residual. Any restaurant that would refuse to ensure you safety isn't a place you should be eating at. They are not outrageous requests.