Businesses should have a moral position, sure.
That moral position should be right? According to who? The business itself? Then that second point is redundant. Everybody thinks their moral position is right, that's what morals are. It's a tautology otherwise.
GitHub employees think their moral position on ICE is right. Many disagree. But according to them that's fine, because they think they're right so should be able to boycott who they like.
Replace Github with bakery refusing to serve same-sex couples. Bakery thinks they're right. Many disagree. But according to them that's fine, because they think they're right so should be able to boycott who they like.
You only think it's a false dichotomy because you personally disagree with the bakery and (presumably?) agree with Github. By saying "the moral position should be right", is you simply saying "and they should agree with me otherwise they are wrong".