I have my doubts. People can learn “critical thinking skills” all they want, it’s the failure to apply them fairly that breaks political discourse at all levels of education.
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.