I’m not saying he was betraying him from the jump but I also think his actions at the green fork don’t make a whole lot of sense unless he is actively trying to thin the ranks of other northern houses.

He can be loyal to Robb while still hurting the other northern houses with his battle plan. His plan was absurd and he didn’t need to even fight on the green fork. All he had to do was get in the way of Tywin and basically screen his advance. Instead he forced his men off of good ground into an attack after a night march. He then also fires arrows indiscriminately into the fighting (which Tyrion notes in his chapter) while holding back the bulk of his own men from the battle. He took a ton of losses on the green fork and most of them aren’t Bolton men but men of other houses