What's next, muslims who eat pork won't be allowed to enter the prayer room? Funnily enough, being an arbiter of religiousness is blasphemy in islam.
The appropriate pork analogy would be pointing out that if you are avoiding pig products, you probably also want to avoid eating bacon ...
Similarly many Jews disagree on the definition of work on the Sabbath. If a Jewish person took off on the Sabbath for religious reasons, is the the employers place to tell them they can't turn any lights on, or use the oven?
So only meat is banned and only when it's not "necessary" (which is really open to interpretation)
It's directly a 1-1 relationship even more than pork and gelatin.
Apples to Oranges, I think, given that both these cases deal with medicine, while your example does not.
To be fair, it could be on the basis of method of administration - I could see someone having religious objections to injections while not having objections to orally administered medicines.
In any case, if your religious objections extend only particularly to the COVID-19 vaccines, there's a good chance that you're not exactly being honest and trying to abuse the rules.