NOTE: CRT isn't really about your skin colour, it's about the system you inhabit. CRT tends to level its charge against the system. Black people can thus become oppressors too. CRT isn't attacking white people specifically, though it does often sound like that. The big claim is that the system itself is racist. Note however that CRT is incredibly diverse. It hasn't been codified into a single system yet.
A famous example of this is the doll experiment in which black infants chose to play with white dolls instead of black dolls. It demonstrates an internalisation of racist ideas. Kids grow up into adults and enact that prejudice. The colour of their skin is irrelevant.
Study: White and black children biased toward lighter skin - CNN.com
I'm not sure how people interpret studies like this.