I work in a resteraunt in Texas (right to work state) where there is a city ordinance that prohibits smoking in the building. The city ordinance is regulated by the health department which do not work evenings. Therefore, late in the evening the managers will sometimes allow customers to smoke cigars or ciggerettes in the building. I am pregnant and have told them that I would appriciate it if on the shifts that I work that they do not allow this due to the medical research that exists that second hand smoke is harmful to fetuses due to the nicotine and tetrogens passing through the mother's blood stream and into the placenta. The managers continue to disregard my request and I have refused to be in the area of the building where they allow the smoking. Can they terminate my employment for making this request?

You need to consult with the City's Health Department to determine whether the city ordinance contains a retaliation or whistle blower's provision.

BTW, right to work means you cannot be forced to join a union to get work. It has nothing to do with this situation.