Here's a thread on that very topic Misterbig: https://allnurses.com/general-nursin...et-449511.html
Short answer is yes, a school can force you. Since unlike K-12 where you are guarenteed by law an education, you are not guarenteed the right to go to nursing school or work in a hospital. That's the bigger reason, most hospital sites require them. If you can't meet the clinical requirements of the hospital, you can't pass clinicals. And hospitals do not have to make religious exemptions.
See the article here at Vaccination Liberation Exemptions, a site/group against vaccinations. Their basic answer, yes, it's pretty much legal for an employer like a hospital to require you to get vaccinated without exception if they so wish: http://www.vaclib.org/exemption.htm#fair
I know of a hospital that made flu shots mandatory last year for all employees that had patient contact. Either you got the flu shot (provided free by the hospital) or you had the opportunity to resign.
Just wanted to provide the information/studied case law and information that I found in my previous research on this topic to Misterbig. My appologies to everyone. I don't mean to pull this thread off topic or want turn it into a debate about vaccinations