Having read a foundational text on CRT (and please go further to read some of the works consulted in the bibliography) you should no longer have a problem with CRT. Yes, it is arcane and difficult, which is one of the reasons that you now know, if you didn't before, that it is no where present in any K-12 curriculum. It is not pitting one group against another; it is explaining how US laws were written to provide more protection under the law to some than to others.
I'm both a person of color and a person of privilege. However, despite what economic and educational advantages I enjoy, I will NEVER have the benefits of skin privilege, which whites, rich, poor, or other, enjoy from birth. I believe that though skeptical, you are smart enough to see and acknowledge that.