It has always been the case that you are only an Israelite if you have an Israelite mother. If there were Israelites that intermarried with the captives brought by the Assyrians their children were not Israelites, and the transplanted populations didn't just become Israelites through marriage. Doesn't work that way. There is no "part-Israelite". You either are or you aren't. This is determined matrilineally, while titles are determined patrilineally. The religion of the Samaritans is a religion of their own. It's not Judaism, they are not Jews or Israelites. They are a remnant of the Arab populations that were transplanted to the land, and whom adopted Judaism (though obviously never completely).
Three Afula residents arrested in right-wing protest (Haaretz)
from the article: Ancient Samaritan sect marks Passover sacrifice near Nablus