Iraq didn't become unpopular until after Bush leaves office in this ATL and Kerry would be overseeing the mess it becomes; Bush would escape all blame.
But it was Bush's war, remember? Dubya wasn't able to escape blame when ISIS started running amuck when Obama was President. Why? Because it was Bush's decision to invade Iraq that created the mess. That understanding would still exist under President Kerry, who like Obama could easily blame Bush for creating a poor foreign policy situation.