I agree that Bile is the key, he becomes the chaos version of Cawl and introduces female space marines into the setting, the chuds can't get angry (tho they still will) because hey it's the "bad guys" who did it, it's out of our hands here at GW "oooooh that tricky Bile he's such a cad"

The chuds are probably dumb enough to get unironically mad at a fictional character and direct their anger away from the new faction