I think you have by omission agreed that perhaps it's possible that CRT is being taught, or something related that could legitimately carry the name is being taught, so I'll address your other points here.

So, can proper context be given to American history without "understanding and analyzing the impact of systems of power, including white supremacy, institutional racism, racial hierarchy, and oppression"?

On the one hand: Yes. Absolutely. If you can't teach American History without resorting to such complicated concepts, you shouldn't be teaching children. The whole effort of teaching children involves simplifying material to retain enough essence to make it worth teaching, while removing as much complexity as possible to make it accessible.

For instance, when the Revolutionary War is taught, you don't necessarily need to go into the geopolitical background behind the relationship between the U.K. and the colonies. It would enhance understanding if you did, but you can describe the conflict adequately without, so if you want to teach that there was such a war to younger children, you totally can.

On the other hand: No. Absolutely not. Power and its application in various contexts, including racial ones, has undeniably played a substantial role in American History, and one cannot understand the causes of many historical events without it.

For instance, the voting laws in the South that disenfranchised blacks after the Civil War were put there precisely in response to the legislative power that blacks suddenly (and successfully!) wielded. Any halfway decent adult understanding of American history should include this, and therefore it should be taught at least by high school.

The key is that different aspects of history become appropriate material at different levels of detail. If you try to introduce complexity too soon, then you are forced to simplify so much that the characterizations given by CRT opponents are very likely to be an accurate portrayal of how the material is taught. For instance, how do you get "institutional racism" across reliably to, say, seven-year-olds aside from saying something like, "White people did a bad thing: they set everything up unfairly so whites get all the best stuff and black people can't have good stuff"?

Furthermore, there's also a choice of how much to stress the positive or negative aspects. For instanc,e when a child is learning to ride a bike, it's generally thought appropriate to be positive, like, "Go on! You can do it! You glided three whole feet that time! You're getting better! Keep trying!" instead of "You're terrible, look how much your feet are hitting the ground, you can't go more than three feet without falling over, this isn't riding a bike at all." The same is true of history taught to children: do we emphasize the triumphs, successes, and improvements? Or the failures, the injustices, and the ongoing problems?

So there's a real debate to be had here. People should feel enabled to contribute their ideas, have their concerns heard and addressed, and dialog should move forwards as these complex issues are grappled with.

This doesn't happen when people are shouted down with "CRT isn't being taught" despite the curriculum supposedly containing discussions of maintenance of racial power, intersectionality, and institutional racism.

So--should all those things you list be taught? Yes, at an appropriate level, at least to interested parties. (It's less clear to me that they all must necessarily be part of a basic high school education, but at least some of them should be.) Should the list that I gave be taught? At least in part, at an appropriate level. But we should be able to talk about it.

Finally, unless you are limited to structuring morality wholly around tribal identity, it is simply wrong that you should necessarily choose your position based on which tribe might gain support from something. If white supremacists happen to actually say something true about race, we should be perfectly content accepting it, not because white supremacists say it, but because it's true. They have a tendency to move very rapidly from true statements to faulty reasoning based on those true statements, or from true statements to lies, but the place to call them out is when they diverge from the truth and/or correct reasoning. This is true even if there are only two sides. And in an issue as complex as this one, having only two sides cannot possibly reflect reality, so it is a strong indication that tribalistic thinking has shoehorned all viewpoints into only two, with the consequence that they're both probably badly wrong. (One, however, may still be far worse than the other.)