Having a giant political flamewar about how critical thinking should work has good potential to result in mutual destruction.
If you really play it out in your head, critical thinking is pretty hard to abuse because it tends to lean away from blind trust.
Every trick that could be taught to get people not to trust your enemy, is one less way you can take advantage of them yourself.
People don’t investigate statements that conform to their biases. And if the statement is something they don’t want to believe, people will deploy the full force of their “critical thinking” toolkit to fight it, while allowing themselves to become vulnerable to all sorts of fallacies and cognitive blinders as long as it only obscures the inconvenient facts.
Further, at least some people will be clever enough to use critical thinking on their own beliefs. Maybe some will only use it to further entrench, but not all. And it only takes a few amazing people to push society forwards; that's all we've ever really had.