Normally, I would say... let people vote with their money. If the general public doesn't like how somebody conducts business with their other customers, don't ever go there; tell your friends not to go there. They will put themselves out of business by their own behavior.
Where this kind of situation gets sticky is determining where personally expression of personal belief and violation of civil rights start to impede on each other.
Yes, the owner should be allowed to practice and express their personal beliefs.
Yes, citizens should be able to walk into any business and receive service that doesn't discriminate against their race, gender, or sexual orientation.
Whose rights are greater?
There's really no good answer go satisfy everybody. The courts have wavered back and forth on whose rights are more important for a very long time. It will interesting to see where the court of public opinion stands on this issue 20 years from now.
Personally, I think civil rights should always win out. Opinions and beliefs can be changed. You can't change what you were born with (race, gender, sexual orientation).