I think that the above graphic, which was tweeted by Neil de Grasse Tyson - and based on data from Fox News(!!), shows an interesting relationship between a college education and who voted for Obama vs. Romney. It also illustrates a pattern in states where higher education and critical thinking is more commonly valued.
I don't have first-hand information, but I would guess that teaching critical thinking is not a part of most high school curricula. It is, however, more common in college, especially university level education. I'll also guess that critical thinking at right-wing colleges and universities is typically not rigorous with respect to this definition by Robert H. Ennis, which is one of my favorites:
"Reasonable reflective thinking that is focused on deciding what to believe or do. ...to seek a clear statement of the thesis or question; to seek reasons; to try to be well informed; to use credible sources and mention them; to take into account the total situation; to try to remain relevant to the main point; to keep in mind the original or basic concern; to look for alternatives; to be open-minded; to take a position when the evidence and reasons are sufficient to do so; to seek as much precision as the subject permits; to deal in an orderly manner with the parts of a complex whole; to use one's CT abilities; to be sensitive to feelings, level of knowledge, and degree of sophistication of others."
I have heard and read comments by people from the right who use the term "critical thinking" as a talking point, but I don't think they really understand the the concept. The right ignores almost every point in the above definition, so much that to highlight the relevant points would require highlighting virtually the entire quote.