Neither the Old Gods, Yss or the Merling King are terribly picky with the sacrifices. He sure as hell will object to them.
He will object to what they do outside of our realm, but in our realm sacrifice of living beings, is tightly regulated to only the worst of evil and non-sentient animals, neither of which he's likely to object to, and he's unlikely to be so inflexible, as to demand we stop allowing the worship of them, a temple of his was in the Opaline Vault after all, and that's a Neutral place if there ever was any, so while there's probably not many temples to evil gods there, temples to neutral gods like ours are probably aplenty.
He's not likely to be exactly happy with them, but he's not likely to object to how we interact with them, which is really what matters, it's no great matter if a priest of Bahamut, clash with Wildling followers of the old gods in the land behind the wall, so long as the conflict don't spill over to our realm.
Bahamut can't afford to make war with Neutral deities, his followers will try to stop the sacrifice of relative innocents if they see it of course, but he has actual evil deities that are far higher on his list, so at most skirmishes will happen, and all those skirmishes will happen outside our realm, to worshippers not working for us, because the worshippers working for us follow our law, good gods aren't incapable of being practical, Bahamut will see that we are keeping the less nice habits of those gods in check, and focus on opposing the evil gods that are spreading misery though the world.
Edit. Not to say he will never raise a stink or cause problems, but he's not going to try to ruin everything, or get us to renounce our association with the old gods, Yss, and the Merling king.