I'm not sure if you're being sarcastic or not?
Crenshaw and others never claimed that CRT and other variants of Conflict Theory were empirical in nature.
In the early 2000s, while pursuing my engineering and applied economics degrees, I focused most of my electives in the social sciences, and actually had several courses in classes where various flavors of Conflict Theory were explored. Essentially, Marx was a Conflict Theorist who focused on class divisions while deconstructing the rather miserable conditions of living in the height of Europe's industrial revolution.
Kim Crenshaw's work was always presented as a lens in which to deconstruct and then analyze various societal conditions.
What I can definitely attest to is that Conflict Theory and it's offshoots are strongly post-modernist in flavor, in the sense where they view attempts at quantifying and measuring to be so strongly biased by the dominant groups of a given culture as to be useless at best and tools of oppression at worst. It's not that they aren't empirical, it's that they are actively hostile to empiricism and reject it.
One of my sociology professors (a true statistically literate prof who specialized in poverty dynamics) used to joke that the CT and CRT folks didn't do research, they just wrote essays that referenced essays that referenced essays.