Why would you want to force someone to touch you, who doesn't want to? Let them do a reduced business, that's their problem.
It may not be quite that simple. What if your religion or other deeply held beliefs also prevents paramedics from touching a woman; or a doctor for that matter? Or what if your religious beliefs extend to excude blacks or orther minorities? The fact is someone engaed in a business that serves the public must make his business open to all who wants to use it or we end up with what American Blacks faced during the segregation era.
You are right about bigots probably cutting off their noses to spite their faces, but that does not mean that they should be allowed to do so.