I would agree that the (economic) policy of the democrats is center-right, but culturally the party definitely has a far-left voice. Radical feminism, postmodernism, anti-racism Mao struggles, gender puzzles. And to use the overused term "wokism".

Wokism is culturally dominant, but widely rejected all the way from center-left to anything to the right of that.

Republicans are economically right (so not extreme right), yet have a far-right outing, as you say.