Prior to the Chinese bombing, the founders of both the Brotherhood and the Enclave were part of the Department of Defense, with the exception of extraordinary circumstances where they were coerced by a single individual into cooperation, they have had extraordinary hostilities?
Technically, the NCR and Caesar's Legion were both descendants the original Pre-War population west of the Mississippi, but that didn't stop them from waging a long and bloody war over control of Hoover Dam-- twice. Shared heritage doesn't stop war, whether it was pre or post bombing, from being conflicts of interests.
It's as they say--- War. War never changes.