It's the "invariant be" - see section 3.1.2 of this paper.
Walt Wolfram contends that usage of the invariant be is age-related, in that young people cease to use it as they grow older. The earliest reference in that paper is a survey of non-standard English by the US Department of Education in 1968 (Labov et al. 1968).
However, that's almost certainly not the first use of the invariant be, but rather when linguistics researchers started to see value in describing African American Vernacular English (AAVE). I suspect that origins of a lot of AAVE, including the invariant be, is irrevocably lost.
The meaning is really interesting, because this is not a simple case of subject-verb disagreement. According to this paper, the invariant be functions as present simple tense in which recurrence is explicitly indicated. Taking an example from the question, "Women be shopping" indicates that women habitually shop, similar to "women shop", except that the habit is explicitly indicated by be.
The present continuous "Women are shopping" indicates that a group of women are currently shopping, i.e. not the same meaning as "Women be shopping".
Based on my reading about AAVE, I would say the archaic usage is unrelated. In archaic usage, "be" is the dynamic verb (e.g. "there be vermin") of the present simple tense, whereas invariant be is a static verb in the AAVE usage.