Have you ever seen the "we reserve the right to refuse service" signs? Those signs allow the owner to turn away clients he/she doesn't want to serve; take, for example, a bar with a customer with a history of starting fights. Does this bar not have the right to refuse service to this man? Why should a florist who happens to be an Evangelical Christian have to serve a gay wedding if it goes against her (wrongly held) religious beliefs? Should this woman I am using as an example have to service the couple just because they approached her first?
These cases aren't comparable. In the case of the bar owner above, he is refusing to serve prospective customers because the latter may represent a threat to his other patrons or his property. The couple in the second case represents no such threats to the owner. The couple are willing to pay the price the business owner sets for services the owner otherwise provides equitably to the public.