Are there reasons to not get a vaccine?

Yes but very few.: There are some reasons depending on the vaccine, called "absolute contraindications." these are very few and your doctor should know if you have a medical contraindication, that is, a reason to not give a vaccine. Philosophical and religious reasons should not be confused with the very rare contraindications.

Yes: It depends on the specific vaccine. The only reason common to all vaccines, is if you are allergic to the components of that vaccine.