Current year military has all sorts of ways to get around it. They'll probably try to start including it during the random jabs you get during inprocessing to basic because once you get into the actual branches you have a lot more options, the easiest of which is just a profile that claims you have an "allergy". That got a few people out of the "mandatory" flu vaccination the rest of us had to get because we didn't think ahead to grab one of those as well, and that was close to a decade ago.