Doublethink is made to force people to accept a paradox as it is, ignoring their logical reasoning in favor of what narrative is being pushed on them.

Zen koans are made to help people explore a paradox, ignoring the need to have a logical reasoning based answer to the paradox. NOT in favor of a particular narrative, but rather to help the thinker see the situation in a new light.

Better question would be, what do they even have in common?