"I maintain that Malcolm X was, for much of his public life, a black conservative."
― Ta-Nehisi Coates, The Atlantic
Black conservatism for the most part has always been a race-conscious response to White Supremacy - not a replica of it!
While black-conservatism can in theory be/become racist, it doesn't mean it is. For most of it's history it has maintained an inclusive (not exclusive) approach to integration, while maintaining its race-conscious identity. One outlier would be the Nation of Islam - a black conservative separatist religious movement.
"Burkean" or "classical" conservatism is not about race. It is an ideological response to the consequences of rapid change in a society. Black conservatism is a response to rapid changes in society brought on by scientific racism, the Atlantic slave trade, and white supremacy.
It is a rationale attempt to righteously engage evil -- not a facsimile of it.