Sorry for overlooking this!
In Critical Race Theory, an Introduction (3rd ed); Stefancic & Delgado (2017), on page 11 they offer the mildest affirmation of the principles: "Minority status, in other words, brings with it a presumed competence to speak about race and racism. The 'legal storytelling' movement urges black and brown writers to recount their own experiences with racism and the legal system." They also mention that there are race-related topics about which "whites are unlikely to know."
Fine as far as it goes, if it doesn't go any farther. But even in the measured legal framework of this book, they cannot restrain themselves from going farther, after describing a picture first of America as largely past racism--describing it as a story--with isolated incidents needing fixing; and then describing as "new accounts" a variety of troubling disparities like school dropout statistics and other negative parts of the experience of some minorities, concluding: "The new accounts dare to call our most prized legal doctrines and protections shams--hollow pronouncements issued with great solemnity and fanfare, only to be silently ignored, cut back, or withdrawn when the celebrations die down. How can there be such divergent stories? [...] critical race theory answers, 'Experience.'"
And at this point it's totally off the epistemological rails. Rather than double down and say, "Okay, there is a serious discrepancy here--what is the actual truth of the matter?", they take a wholly different tack to addressing the issue: "Literary and narrative theory holds that we each occupy a normative universe or 'nomos' [...] from which we are not easily dislodged."
Firstly, if you want to understand how people change their point of view, you should be looking first to cognitive scientists and psychologists, not to literary theorists. And secondly, reality just got dropped on the floor here. They do halfheartedly pick it up again a few lines later, but this illustrates the epistemological danger.
One doesn't have to dig too deeply to find the functional nihilism seeping in further. In Towards a Critical Race Theory of Education, Ladson-Billings & Tate (1997) (https://www.unco.edu/education-behavioral-sciences/pdf/TowardaCRTEduca.pdf), the authors describe the issue as such:
Challenging Claims of Neutrality, Objectivity, Color-Blindness, and Meritocracy. A theme of "naming one's own reality" or "voice" is entrenched in the work of critical race theorists. [...] Critical race theorists argue that political and moral analysis is situational--"truths only exist for this person in this predicament at this time in history". For the critical race theorist, social reality is constructed by the formulation and exchange of stories about individual situations.
The authors apparently approve, going on to embrace privileged racial knowledge, too:
Without authentic voices of people of color [...] it is doubtful that we can say or know anything useful about education in their communities.
Tate and Delgado and Stefancic are among the more studious and cerebral of the CRT crowd (I'm not familiar enough with Ladson-Billings to say), especially when you consider its outgrowth into an anti-racist social movement, not just a type of legal or education system analysis. (This outgrowth is natural and expected, as perhaps the distinguishing feature of critical theories is that the theorist is also supposed to be an activist, at least according to their founders e.g. Horkheimer. The affinity for narrative in CRT also echoes the same epistemological defects in critical theory.)
The problem is not that narrative can't be valuable. The problem is, rather, that it is too natural for us, and that we need constant reminders to be precise, check our facts, collect statistics, and so on, in order to gather a reliable picture of objective reality. To exalt story over study is to start upon the path to the death of knowledge. The rigors of the legal framework bring legal CRT scholars back off that path time after time. But outside of legal settings, the task falls to us to insist that anecdote has only the power that anecdote should, regardless of whether one is white or black, whether one is speaking one's truth or telling one's lived experience. There is now much of CRT outside legal settings.
I hope this has adequately addressed your request for references.