Jewish holy places in Israel belong to all Jews of every denomination and kind. Some Orthodox Jews do not even believe in the State of Israel. The issue of the wall is fascinating in that no one actually can prove that it was part of the Holy of Holies, the place where the two tables of commandments rested. All other parts of the Temple were places where worshippers could congregate. They were not holy. There is no mention in the Torah about the right time or place to wear a tallit. Women, according to our history. have the same rights as men. It was the men who chose several women to lead Israel, from the days of Deborah until today.
According to the Torah, you are a Jew because your father was a Jew. The rabbis changed that, and since the days of the sages, that has become the rule. The Torah does not differentiate between the sexes regarding the tallis. The Orthodox follow rabbinic interpretations of the Torah, as do many other sects of Judaism. Many Jews do not believe in man’s interpretation or man’s improvisation or man’s many additions. The prayer wall has no meaning to them. The reality is that God gave the Jewish people their wish to have a Temple like those of the other religions. They wanted a place for their God. God gave them that chance several times and finally decided enough was enough. The Temple became the focal point of Judaism and God decided that was not what Judaism was all about and had it demolished. God should be in the minds and hearts and deeds of man, not in the remnants of a wall or pieces of paper in cracks of that wall. Some pray at the wall bemoaning the days of its destruction. The past is past. God judges man by deeds not prayer no matter what the place. The words inscribed by the finger of God are ours to observe in mind and action. All else is of little importance.