"Yes. As I said, "there were members of the 10 northern tribes who fled into Judah as well. So present-day Jews are really descended from all the original tribes, not just the tribe of Judah.""
I do not disagree that both houses are represented in Israel of today but the majority of those of the House of Israel are not there there is not enough real estate in that land to have them alll move there.
That majority of the House of Israel are the 'lost sheep' that Christ refers to. They do not know who they are and most call themselves gentiles!
They do not know who they are and most call themselves gentiles! It is most likely that, after all these generations, they are all gentiles. Sure, there is the possibility that some could be halakhically Jewish (or 'Israelite', if you prefer) and not know it, but there is no way to know for certain. Which is why, when these cases have arisen, formal conversion has been the usual option.