They have a point, for the most part. You need to be able to see the flaws in something even when you enjoy it.

Though, the second portion's a bit off. I've seen plenty of instances with people bringing up racism and the like when there isn't any to try and tear apart a form of media. Or they'll shout out, "that's racist, don't ever let anyone see it again!!" and try to act like it never existed instead of acknowledging the flaws of the time and letting others learn that it's bad and why.

The addition of race and other such things in the examples doesn't seem necessary as a broad term one is simply able to criticize everything for whatever reason and still enjoy it. Adding the angle of race and presupposing the motivations who might disagree is a bit rude but perhaps I've not wasted enough time on tumblr to actually see the accusations manifest.
It seems an unnecessary way to politicize something, if someone enjoys it and doesn't want to be criticizes it generally doesn't matter the angle unless they see the critique as wholly ridiculous.