Burning? No. But what’s taught in school, what’s taught about it, needs to be considered.
And what’s allowed on school (in particular, graphic pictorial pornography, and anything actually illegal) could include not allowing some things on campus.
Once again I’m a bit startled by your choice of framing a question, i.e.: “And of course on the left there has been plenty of call for books to be removed from curriculum if they’re “problematic” on race or gender or history.” – If you mean, say, history books that would whitewash American history, or science books that would say that creationism is an equally scientifically valid theory compared to geology and astronomy and so on, then while I would not “ban” such books from schools, I think the accurate, truthful and responsible thing to teach about those is that they are inaccurate disinformation by certain socio-political groups, and that’s not “the left”, it’s just not the willfully misinformed faction of the American right.
That could be objectively followed up with lessons about recent attempts to cloud what actually well-known to be true, for political reasons, and the cultivation of a culture of lies by the right-wing, etc.