At the risk of doing "no-true Scotsman", that isn't my reading of the left. The left I know dumped both Al Franken, a liberal, and Lena Dunham, a "pop feminist"[0]. The left I listen to also speaks regularly against people like Ben Carson, it's not like just because someone is in an identity group they are automatically believed/revered, their point of view/character/deeds are taken before their group.

For "whites shouldn't talk about racism", I think that is sort of a mischaracterization of what people say. People should realize that they cannot fully appreciate things outside of their experience. That's a logical thing, not a leftist thing.

[0] Not sure how else to describe her.