re:take the pill and be fired
Since when does a company have the right to impose it's religious beliefs on its secular employees.? Separaton of church and state is there for a reason.
Since the dawn of time, that's when. Companies have always been able to impose their beliefs on their employees, there's no law prohibiting it. In fact, there are laws preventing the government from prohibiting it, it's called the 1st Amendment, which you mention in your second sentence.
The 1st Amendment applies ONLY to the government and does NOT apply to private citizens or companies. If I owned a business and I wanted rules that followed Christian beliefs, or Sharia law, or any other religious rules that you want to think of, I can do it legally, because I own the business and I determine what its rules should be. The only time that doesn't apply is when I accept federal money and there is a stipulation to accepting that money that I can't do that. Then I decide whether or not to impose the government's restrictions or not by accepting or not accepting that money.
EDIT: The rules I apply to my company employees mustn't violate civil or federal laws but as long as that criteria is met, then I can do pretty much as I please in my own company. I can not hire a person if they smoke, I can fire someone on moral grounds etc.