So I'm confused--are you saying that Israel thinks Messianic Jews are not Jews because they abandoned their faith or something like that, OR are you saying that Israel doesn't let Messianic Jews to be citizens because sometimes non-Jews convert to become Messianic Jews?

It sounds like a variation of a - not so much that they abandoned their faith, per-se, but that the faith they espouse as being Jewish is not acceptably ‘in the same room’ as other Jewish faith.

It would be somewhat like saying you were a Messianic Christian because you believed that Mohammed was a later prophet. There is a word for that kind of religion, and it isn’t Christianity.

Israel basically sees them as evangelizing Christians in disguise. They don’t consider them Jewish because they both proselytize and worship Christ as the Messiah. Both of those things are offensive to the traditional tenets of Judaism.