I disagree. If Joe works as a waiter for a restaurant for 10 years, and then the restaurant gets a liquor license, can he refuse to take orders for alcoholic beverages or refuse to take drinks with food because his Baptist or Wahabi religious beliefs are against alcohol?
While the particulars of this case (abortion) make it interesting, the general principles are employer vs employee. And in the US, it is the employer that usually wins - employees generally work 'at will' of the boss, and can be dismissed for almost any reason, especially those characterized as insubordination or a refusal to carry out the assigned work. Its called capitalism.
Only thing to do is find another employer.
>> If Joe works as a waiter for a restaurant for 10 years, and then the restaurant gets a liquor license, can he refuse to take orders for alcoholic beverages or refuse to take drinks with food because his Baptist or Wahabi religious beliefs are against alcohol? <<
It's an issue of reasonable accomodation. In your example, such a restaurant depends on drink sales for its profits, so if she won't sell licquor, she is fundamentally incapable of doing her job at all.
Here's a better example: Tina has been waiting tables at a restaurant for years. The state law is changed making it easy for restaurants to get licquor licenses, so even the restaurant normally caters to families with kids and doesn't serve alcohol, it obtains a licquor license in case someone wants to hold a reception there or something.
Tina says she's a Baptist and cannot sell licquor. I would say that it would be reasonable for the restaurant to simply not schedule her to serve the function room when there is a party there.