The intellectual justification, inasmuch as there is any, for what the right is doing has come almost entirely from leftist thinkers, though.

The right absolutely does make truth-claims in the service of enhancing their power. But you don't beat them by going all Foucault on them. You beat them with Popper. Or, heck, Descartes.

The current social dynamic turns a straightforward game of "the right is flat-out lying" into a confusing mess of "I am an oppressed class speaking my truth, and the right is less oppressed so who cares what their truth is".

It's completely bonkers.

The moderate left is still a reasonable place (as is the moderate right, but the moderate right is almost extinguished these days), but they've lost most of their rhetorical force against the right by not cleaning up their own house when the illiberal far left says nonsense. The tu quoque fallacy is a fallacy, but it's still good strategy to keep the right from employing it extensively and with glee, as they can now.