I'm open to correction on this, but I don't think the religious establishment has anything to do with it. As I understand the law, based in large part on the Reich, if you're "eligible" to be persecuted as a Jew, based on ancestry not faith, you can immigrate. If you've taken (and acknowledge) another faith, no, you can't, since you're not open to persecution as a Jew. Which is alive in 2013.
Not as much a religion thing as a persecution thing. I don't think Rabbis are involved at all.
The Reich, I think, didn’t care if you took a different faith. They believed Jewishness was a genetic disease that had to be eradicated by killing all carriers of the gene.