“all civil rights” meaning you have full civil rights but can't force a private company to give you a job when you refuse to follow safety rules? Especially in a country where employers pay for healthcare it doesn't seem unreasonable to require a safe, easy, and highly effective means of avoiding very expensive treatments.
This is also far from unprecedented. I've worked at jobs which required other vaccinations, schools all around the country require a ton of vaccinations, and the people who don't want to do that for whatever reason have always had the option of homeschooling, finding another job, etc. If this is such an important issue to you, take responsibility for the consequences of your choice — there's certainly a long tradition of people accepting that as a cost of their religious decisions.