The religion issue is more germane given that it's an explicitly Catholic institution. It at least seems that would be more like Eich being revealed to have lobbied against open source licenses and net neutrality: in a direct conflict with defining policies of the organization.

(Or is it? I don't have a good feel for how important it is doctrinally as opposed to socially. Presumably it would be reasonable to dismiss him for, say, publicly denying the divinity of Christ, or saying he thought the Trinity sounded kind of unlikely. I don't know where the doctrine re sex and marriage falls on that scale.)

On the other hand, if the school has a policy of not discriminating on the basis of sexual orientation as he says it does, that makes a big difference.