"You have examples of these folks harassing business owners...."
Of the top of my head, no.  However, I do know of some conservative talking heads that have for years been  convincing their devout followers that there is a war on Christmas because business have chosen to have their employees tell customers "Happy Holidays" instead of "Merry Christmas"....as if someone wishing another "Happy Holidays" keeps that one from celebrating Christmas.  Heck.....at the BSA Jamboree, Trump made it sound like saying "Merry Christmas" had been banned and was illegal to say....and that he was going to fix it.

"...asking the government to force service or fine them out of existence?"
Discrimination based on sexual orientation is illegal by law.  If they didn't want to be fined, then they need to follow the law.  If a fine made them close their business, then they weren't in very good shape to begin with.  

Just out of curiosity...who was fined out of existence for breaking the law?