Most of our high schools despair of teaching mathematics to the level of algebra, to most of their students. Many haven't yet despaired of conveying literacy to those same students, but the outcome is by no means certain. I would consider both of those prerequisites to "critical thinking", no matter what particular idiosyncratic definition of that phrase you might prefer. Therefore I suggest that we aim lower, for a sort of animal suspicion that comes naturally to all humans. The result, from the perspective of political harmony, will be the same: hundreds of millions of critical thinkers would not magically all arrive at the same conclusions on any set of topics. In a perfect world of critical education, not only would you still disagree with most people's conclusions, but you would also still disagree with how they arrived at those conclusions.
What country are you writing from, and could you give some specific examples?