It's not a question of "should?" It's a question of "do?" And the answer is "no."
Look at the Boy Scouts. The only reason they got out of letting gays be Scoutmasters is that they sold the Court on the notion that they were a religious organization. A commercial enterprise, though, is not a religious organization, even if the boss is religious.
As an aside, it was a pretty dang close case even with the Boy Scouts. A 5-4 decision.
You're confused. The Boy Scouts didn't convince the Court that they're some sort of religious organization. Religion had nothing to do with that case at all. They won because they're a private organization with a 1st Amendment right of expressive association. Meaning, they can exclude a person from their group if that person doesn't share their views or advance their message and goals. Pretty much the way Jim Robinson gets to pick and choose who he wants participating on this forum. He can't Constitutionally be forced to let the moonbats post here against his wishes. Free association--it's not about religion; it's about about freedom to choose the people you want to be around.