What form is the "be" in "be that as it may"?
It appears to be an archaic form that has persisted as a colloquialism in modern English. "Be" is the verb "to be", connected to "that"; so the phrase essentially means "That is as it may [be]...".
To address your comparison to "Let that be as it may...", you could reasonably understand it as an equivalent to "For the sake of this discussion, let's say that's true..."