A Jew is anyone born of a Jewish mother or Halakhically converted to Judaism, regardless of belief or lack of it. If atheists, b*ddhists, and pagans can be Halakhically Jewish I see no reason why that adjective should be denied to "Hebrew chr*stians."
I am aware of all the other things you said. However, my point was that Qara'im and other small-o "orthodox" heresies are never included in the "branches of Judaism," which always consist of Orthodoxy smothered by liberals.
I once met a young man who believed the Written Torah was from Heaven but who rejected the rest of the Bible (as well as the Oral Torah) and even rejected the doctrine of an afterlife. While he certainly was not an Orthodox Jew, I fail to see why his belief system failed to qualify as a "branch of Judaism" just as much as "reform," "reconstructionism," and "secular humanistic Judaism."
I once met a young man who believed the Written Torah was from Heaven but who rejected the rest of the Bible (as well as the Oral Torah) and even rejected the doctrine of an afterlife. While he certainly was not an Orthodox Jew, I fail to see why his belief system failed to qualify as a "branch of Judaism" just as much as "reform," "reconstructionism," and "secular humanistic Judaism."
This is a due to the arrogance of the more established Jewish communities.