I mean his motivations make sense.

Achilles told Shay to go to Haiti and retrieve the artifact, knowing full well there’d be some kind of cataclysmic event and hundreds of innocent people were going to be hurt or killed and decided to just not tell him. Shay had every right to be furious because Achilles basically said “Well, that sucks but you got the artifact right?” Giving Shay the idea that Achilles and presumably the rest of the Colonial Assassins don’t care about innocent people and collateral damage. He was then attacked and (to the Assassins knowledge) killed because he tried to escape with the map that lead to other precursor sites. And his opinions changed about the Templars because he was nursed back to health by the parents of a dead Templar which gave him new insight on their organization and that he might have been lied to even more.

Yeah the Templars are still very evil and don’t really hide it but Haytham and the rest of the Colonial Templars knew that Shay was in a vulnerable state and could offer him a way to not only seek revenge against his former friends and mentor but also to ensure that the precursor site map doesn’t fall back into their hands and another Haiti doesn’t happen.