There's a double standard to this, both internally in the people that refuse service and also the activists themselves.
People who cite religious beliefs, like in the florist case, also simultaneously make the statement that providing flowers to a Muslim/Atheist marriage doesn't necessarily constitute an endorsement of Islam/Atheism. Consistent logic would dictate that making flowers and baking cakes for gays doesn't then necessarily constitute an endorsement of gay marriage.
That being said, LGBT activists have a vindictive tendency to specifically target these businesses when others or better ones exist. Like the two who tricked a Christian Pizza place into catering an anniversary party. First, who the heck wants cheap pizza at an anniversary party? Second, it smacked of antagonism.
They also don't target anyone else. I don't see LGBT people running into Islamic stores and demanding their services. Why the hypocrisy? Why only target Christians and not other religions and groups that are objectively WORSE on LGBT relations. If any group needs to be "forced" to comply with tolerance via legislation and fiat, it's Islam/Muslims.
The only person I've heard of doing that is Steven Crowder, and his reception at the businesses in question was far worse than anyone who strongarms some old fundie store.
We have this really weird and potentially dangerous notion in our society that we can force people to be "better." You can't. The line between good and evil runs through every human heart, and things like this create a precedent which will be used in all sorts of far more catastrophic ways in the future. Just don't shop there. Go somewhere else. If people just avoided stores ran by fundamentalists, they'd all eventually go out of business.
They only stay in business because LGBT activists do this crap, stir up a fuss, and then reactive groups change patronage to the businesses in question from their typical M.O. in an effort to show solidarity.
