Critical thinking is only part of the problem. There is a problem with understanding that we really are equal, no matter how we look and who and how we worshop, or even worship at all. Even if there is no profession of privelage by certain groups, there is certainly a difference in treatment. Let me expound a bit.
White, black, yellow, should not make a difference. Yet black neighborhoods are called "bad neighborhoods", and black politicians get voted for by blacks, whites by whites, and so on. Even socially - interracial dating is rare, as are interracial friendships it seems. In effect, we treat each other based on superficialities, whether we admit it or not.
Allah, God, YHWH, Vishnu, no-God - should not make a difference. And it does. Atheists can't get elected. Muslims are suspicious by default.
Basically, we have a severe kindness and respect deficiency in America. Teach Critical Thinking? You bet. Don't hang your hat on it solving the divisions in American Society, however. Teach kindness and respect to all people also - and whatever else needs to be taught to repair divisiveness.