That's actually easy.

All you have to do is ask if they're being consistent.

If they've taken all the vaccinations to this point but suddenly have an issue with this particular vaccine, then it's not a religious thing. Personally, I don't feel like it should matter whether a belief is fundamentally religious or not. The thing that matters is that a person believes it.

That said, if they aren't being consistent, then there's no reason to take them seriously.