First of all, one should say, that there are no general answers that can be given concerning this matter, such as “with an allergy you mustn’t – or you must dive in any case”! Depending on the allergy, the attending physician during the medical examination for diving fitness will always make a case-by-case decision. Thereby, it also depends on the region where you have the intention of diving anyway. An allergic reaction, which can be caused by pollination at home for instance, can again subside in a diving area at the Red Sea for example and as such this can be completely trivial for diving.
For further information, a diving doctor should definitely be consulted before undertaking the trip.