Switched to creative from survival, and the Pillagers attacked with their crossbows. This was endless until they were killed. 
I have noticed, also, in long-term testing, that Pillagers seem MORE attentive than other mobs while in creative, even if they are not attacking the player. They turn toward the player more often than other mobs, and rarely wander off if a player is present. I imagine this is relevant to them attacking the creative player.