In HaBayit HaYehudi, the old "Haskala" discussion is taking place. Do we stress Atzmiut Yehudit, or Zehut Yehudit, independent of religion, or not? The rational answer would be "no," of course religion is critical in Atzmiut Yehudit. The latter falls without the first, there is nothing to keep it standing. And the reply would be that in reality "Atzmiut Yehudit" and "Zehut Yehudit" exist independent of "religion" as determined by "the rabbanim." And what if the "religion" falls because it is intellectually doomed?
At the end of our Parasha, at the very end of the book Bereshit, we read about Yoseph's adjuring the sons of Israel to not forget to take his bones, his Atzamot, when G-d will redeem them. The source that is talking here is E. Indeed, we see in a later part of E, Shemot 13:19, that Moshe takes the Atzamot of Yoseph. And the GR"A comments that Moshiach will similarly take the Atzmiut of Moshiach ben Yoseph.
Of course, the Atzmiut of Moshiach ben Yoseph can not really be, just like Atzmiut Yehudit can not really be. And the GR"A does not explain what Moshiach will do with the Atzmiut of Moshiach ben Yoseph. Maybe he could not. But my conclusion is that, in the current time, it is very healthy to stress Atzmiut Yehudit independent of anything, and "Chiloni" Jews should be totally welcome in HaBayit HaYehudi. We are in the middle of a process. We are not at its end.
