yswo,
First, Medinat Yisrael annexed East Jerusalem, so as far as it is concerned the Kotel Plaza is under its jurisdiction.
Second, Jews should be able to visit Jewish holy sites — including Machpelah and Kever Rachel — no matter whose sovereignty is manifest. The problem was not that Machpelah was a mosque but that Muslim rulers did not permit Jews access. The Israeli government by its declaring it to be a “National” site misses the point. Jews should have been able to visit the Kotel, Kever Rachel, and Machpelah prior to 1967.