With regard to Ashers Bakers and the gay marriage-promoting cake, there are clearly two sides.
Some believe that people should have the right to decline business that is contrary to their beliefs. Just to make it clear again, not to refuse to serve a certain class of person, but to refuse a certain morally significant sort of business.
Others believe that people should never have to encounter businesses acting on views contrary to the own. Businesses should have no right to refuse orders that they consider immoral.
I don’t think anyone seriously suggested the second view until gay rights activists have championed it in recent years. And, as usual, government agencies follow suit.