E. D. Hirsch Jr. is one of my favorite education theorists. I find that cultural literacy makes intuitive sense to me with its emphasis on things that children should know. While Hirsch often gets accused of trying to promote "white education," his goal has been to help children of color. If you live in a society founded upon European culture and you wish to function within it then you are going to need to know the things that members of the dominant culture take for granted. This does not mean that there is anything superior about European culture nor does it mean that American culture cannot or should not change to reflect the greater diversity of its people. One adapts to the world around oneself.
Having a common set of cultural references functions in much the same way as language in allowing for a functional democratic country. A monarchy can function and even benefit from the fact that the peasants in different parts of the country speak different dialects and would not understand each other even if they were to meet. A democracy, on the other hand, needs a population capable of deliberation to at least come to the belief that they are one people with a mutually understood common good that all parties can be trusted to sacrifice themselves for. In practice, this requires that people have a common language that allows them to understand each other.
In truth, it is not enough that people speak a common language; to avoid people simply speaking past each other, it is important that people also have a common set of cultural references. For example, being familiar with Star Wars to the point that you take being called "rebel scum" as a compliment, shows me that you have a deeply ingrained sense that it can be legitimate to oppose certain kinds of authority. This can serve as a useful foundation for political cooperation. From this perspective, it makes sense to teach Star Wars in school in much the same way that we teach Shakespeare. (Schools can even use Ian Doescher's Shakespearian adaptations of Star Wars.)
Following Hirsch, I am skeptical of claims to be able to teach critical thinking as it is difficult to evaluate. If students are unable to say who the American Revolution was fought against, I am inclined to assume, barring evidence to the contrary, that they are incapable of coming up with coherent arguments in favor of democracy or monarchy. Furthermore, my cynical self suspects that the push by schools to teach critical thinking is a cover for their failure to actually teach. If schools can pretend that they are teaching critical thinking (and there is no easy to prove that they are not teaching it) then the fact that they objectively fail to teach basic facts about the American Revolution cannot be used to reach the obvious conclusion that the school is a waste of the students' time as well as the tax payers' money and should be dismantled.
Similarly, it is a dead end to try to teach reading in the abstract. Students can never become good readers in general but only good readers of specific subjects from which they have mastered the necessary vocabulary and references. To do this, students need to do extensive reading in those subjects. Along the way, they should be aided by teachers who are themselves well-read in the particular subject and understand the particular vocabulary and references that are necessary to make sense of the material.
An area where I disagree with Hirsch is that Hirsch favors a highly centralized school system with a set curriculum that does not change from teacher to teacher and school to school. To be fair to Hirsch, he is not a libertarian and has no prior commitments to limiting government authority. Furthermore, there are practical reasons to support top-down curriculums. It simply is not workable to expect teachers to design their own curriculums that are going to effectively teach state standards. It is one thing if teachers are simply expected to offer courses on their eccentric selves (not necessarily a bad method of teaching) to allow them the liberty of teaching whatever they think is worthwhile. If we expect teachers to fulfill specific goals then they should be given PowerPoints, videos, and assignments to teach that information.
From a social or political perspective, it makes sense to not only insist that teachers in the same school teach a common curriculum but that all schools in a city, state, or even country teach the same curriculum. If you want a unified society or country then students are going to need a common set of things that they can assume that everyone else knows as well such as the English language or Star Wars.
As a secessionist, I believe that the diverse people currently living in the United States would be better served if the country were to be divided. This would end the culture wars and allow everyone to live in a country designed to suit their particular tastes. As such, I believe in the importance of cultural literacy but it serves a different purpose for me. Instead of using cultural literacy as a normative claim that everyone should have a set of common cultural references to allow them to function as part of one country, I see cultural literacy in positive terms. Where should we draw the lines for the different "un-United States?" A useful place to start a discussion would be to privatize education and see what kinds of curricula different schools would create. Those schools that developed similar curricula based on similar cultural references should likely remain as part of the same country. Those populations that clearly have different cultural references to the extent that they would not want their children taught in the other group's school system should split up.
It is obvious to me that the Hasidim of New Square or Kiryas Joel should be given their own country. One can see this simply from the fact that they want a different kind of school curriculum for their children based on making sure that these children grow up without cultural references like Star Wars. I am also willing to accept that people who want their children taught a 1619 Project or a Howard Zinn version of the American Revolution should also belong to a different country from me. All of this can be done peacefully and would actually help different groups live with each other. I can be perfectly tolerant of people with radically different political values from mine when they live in a different country. It is when we have to share a country that we are at risk of conflict.