Yes, I and my friend used a similar argument and we both got accepted. Basically, you need "It is my sincerely held religious belief" and make sure you don't mention any personal beliefs about the vaccine or how they need to act. Don't give them ammunition to say "this person is just an anti-vaxxer" and don't explain why you aren't an anti-vaxxer. Only give religious examples.

For example, We used the catechism of the catholic church on morality and conscious decisions.

and how because of the vaccines using directly or indirectly aborted fetal cell lines, using the catholic catechism, and my moral judgment developed through my catholic faith leads me to believe that taking such vaccines is immoral and sinful.

something along those lines.