No business man has to carry anything he doesn't want to sell for whatever reason he choses not to sell it.
You must not be in business for yourself, or else you'd understand what is already obvious to most business owners.
I suppose you'd also tell an obstetrician who refuses to perform abortions to "find a different line of work" too, because he's interfering with reproductive "rights?"
Maybe more on your brain level, by your same logic convenience store owners must also be forced to sell skin mags, cigs, and condoms, because others do, and if they won't, you think you are in some position to tell them to "find a different line of work."
In my store you're one of the easiest kinds of customers for me to handle. I'd just tell you to get out of my store and don't come back. Your business wouldn't be missed.
So you are in the business of throwing out customers because you do not like their opinions or you refuse to do business because you disagree with their needs? Assuming this was a pharmacy, if you were to throw me out, make sure that I would not be the only customer you lost. I'd make sure your reputation, based on my experience, would be ruined and find ways of having your pharmacy liscence revoked. It would make you divert time and energy away from you operations, regardless of its success. The pharmacists is there to serve patients, not evangelizr their morality on others.