Here's the thing, there is a difference between refusing to serve someone based on sexual orientation and refusing to participate in an event that violates your conscience – relgious or otherwise.
Sadly, too many people are confusing or conflating the two. The various shops that have refused to provide a service to a so-called same-sex wedding event have done so because it violates their conscience. This is well within their rights. In the case of elderly florist and the bakers, each served the very same customers, regardless of sexual orientation, in the past but refused to participate in these nuptials. They did not refuse based on orientation but based on the fact that they would be materially participating in said event. These businesses even made attempts to accommodate their customers by referring them to providers that would have no issue participating in the event.
The conscience and religious beleifs of these individual business owners was violated as per the First Amendment. However, the rights of the customers were not because they could still be served, and likely were, by another provider and were welcome to return for any other reason and receive service except for those that violate the conscience of the business owner.