How far would that go, though?
Suppose, for example, I believed that hair was sacred so refused to be shaved before an operation? (I'm not sure this is entirely silly, I'm fairly sure a similar belief leads Sikhs not to cut their hair or shave their beards, though to my knowledge it hasn't affected operations on Sikhs.) But shaving the hair is important for Hygiene, no?
Or alternatively, to extend the transfusion argument, I refuse all transplants too? Maybe out of some idea that I was given this body and have to use only what was originally given (overlooking the fact that there's probably not an atom of me that was still there ten years ago).
Does the personal view become less important if it's just an individual one, or conversely more important if it's part of a shared culture? Should some ideas that are known to be wrong be respected just because a fair few people share them? Where, if anywhere, is the line drawn?