Ok but dropping the National Enquirer would make Amazon look even worse. And keeping National Enquirer doesn't make Amazon "look bad"... you are mixing issues

Ok but dropping the National Enquirer would make Amazon look even worse. And keeping National Enquirer doesn't make Amazon "look bad"... you are mixing issues here. National Enquirer itself may not be pro-Amazon, but they'd be that way whereever they are hosted. Their existence on AWS, though, does not impact Amazon one way or the other, because even those who dislike what they publish, aren't generally claiming they should be denied hosting.