Yaaaaawwwwwwwwwwn ... analogies must be analogous. ChuckyLarms' hypothetical is not. Here are several which are analogous to the case:
A vegan restaurant cannot refuse to serve an omnivore, but omnivores cannot force the vegan restaurant to serve meat or cheese or honey.
A Jewish kosher fish monger cannot refuse to sell to non-Jews, but non-Jews cannot force the fish monger to sell shrimp.
A Christian website designer cannot refuse to design a website for all gays, but gays cannot force the Christian to violate his/her religious beliefs
A Halal restaurant cannot refuse to serve non-Muslims, but non-Muslims cannot force the Halal restaurant to serve ham.
A black-owned dry cleaner cannot refuse to serve whites because they might be racists, but a KKK member cannot force the dry cleaner to clean Klan robes. H/T ACLJ
IRL, the website designer had done work for gay/lesbian business people, knowing they were gay/lesbian. The designer refused to do a website promoting a same-sex wedding in violation of his/her Christian beliefs.