They can... Might not be common in US but common Europe... Doctors especially Consultants want little to do with guys that deliberately sabotage their own health...I never heard of that. I don't think it's real common, unless I'm just out of touch. I mean, they are into making a profit.
Saying that there is a very simple way to solve this... If you don't want to take the vaccine, I will respect your wishes as long as well all have to tell our Insurance provider, let it be treated like smoking... It is a chose and you just pay for your lifestyle choice...