If you refuse immunizations for your children, once they are in school you are forced to sign a waver stating that you refused shots due to religious beliefs. Failure to sign this paper will result in the child not being accepted to attend the school.
So, if you're up for a big hassle every year, yes, we still have the right... sort of. They just make it a big pain in the butt.
Also, I've known jobs that require you to be current on your shots, failure to have them will result in you not getting certain jobs.