I believe there is a problem with the way race can be taught in schools, but it just isn't the exact problem conservatives are honing in on.
Conservatives are tarnishing the concept of Critical Race Theory as a whole because it's an academic (sub?)field within higher education...and they view colleges as bastions of liberal elitism that are monolithically hostile to conservative worldviews. They'd either prefer that universities expunge critical thought altogether...or that those universities would begin to actively teach conservative exceptionalism.
However, there are individual educators who make the mistake of teaching about racism and race relations by attempting to hold their White students personally culpable for the ugliness of American history, while sometimes infantilizing students with Black, Indigenous, Latino(a), and Asian heritage. This is *not* CRT. It's simply teachers who are so overcome with their own white guilt that they're abusing their power to take out their own "issues" on their students. This is harmful, and it needs to be called out / stopped...but it isn't necessarily part of a Critical Race Theory curriculum.
When looking at actual CRT itself: I think a big point of the overall contentiousness, that often doesn't get discussed/framed in an honest way, is how racism should be defined. Some/many CRT proponents will allege that racism can ONLY be systemic in America. Many conservatives take the diametrically-opposed extreme -- that racism is apparently no longer a significant problem (or "much of a problem"). And many centrists, such as myself, acknowledge the systemic forms of racism that oppress BIPOC Americans, while *ALSO* acknowledging that racism can be cultural or social (including instances when it might be directed against White people) -- in other words, two things can be true at the same time; the various iterations of racism out there just require different solutions to combat them, based on context.
When certain individuals -- from whichever side they fall on -- attempt to unilaterally commandeer the entire narrative, that's when all of the gaslighting, "canceling," and character assassinations commence. I think this dynamic is really at the core of this whole conflict...and the stigma conservatives have placed on the CRT moniker is just a distraction employed to oversimply a very complex problem.