A question for Catholics

I was just reading a post over at the blog Pharyngula about the Catholic ceremony of the Eucharist when a question popped into my head that I can not quite resolve. If a Catholic who whole heartedly believes in the processes of transubstantiation (the communion wafer and wine actually turning into the body and blood of Christ (not to be confused with consubstantiation, where only the 'essence' becomes Jesus bits)) happens to be a vegetarian? Granted this question is mostly tongue-in-cheek, but it does make you wonder. If the person truly believed what they are eating has become the flesh and blood of their deity and the person is disgusted at the thought of consuming flesh (granted not all vegetarians are disgusted at the thought, but it sounds better here), then how would this work? I would imagine a true believer would make an exception but the thought has to be there in the back of the mind somewhere.