Not Israelis - but Jews.
From the New York Times, January 4, 1964:
All of Jerusalem is holy to three religions—Christian, Jewish and Moslem, and some of the religious sites in and around the Holy City are shared by two or even all three of the religions.....For the Jews, the holiest place is the Wailing Wall, where —until excluded after the Arab-Israeli war of 1948 — they lamented the destruction of the great Herodian temple of 40 B.C....Another holy site shared by the three religions is the tomb of the patriarchs Abraham, Isaac and Jacob, which is situated at Hebron, south of Jerusalem. Christians and Moslems still go to the big mosque in Hebron to pay their respects to the patriarchs. Since the Arab-Israeli war it, too, has not been accessible to the Jews....Somewhat in dispute is the Tomb of Rachel, the wife of Jacob. According to tradition, Rachel died here in childbirth and Jacob erected a memorial over her grave.Still visible is the place on the wall where the Ten Commandments and prayer shawls were believed to have been hung. The Jews have not been permitted to visit the tomb since 1948.
The head of the largest organization of Orthodox rabbis in the country appealed to President Johnson tonight to use his influence in the United Nations to get permission for Jews to worship at the Wailing Wall in the old section of Jerusalem occupied bv Jordan.Specifically, Rabbi Abraham N. AvRutick, president of the Rabbinical Council of America, urged both the Federal Government and the United Nations to enforce a provision in the Jordan‐Israel armistice agreement “which affirms the Jewish right to access to the Wailing Wall, and to all sacred Jewish sites and shrines in old Jerusalem.”...The rabbi also cited the Israeli practice of permitting Christians to go through the Mandelbaum Gate on sacred Christian holidays to visit holy sites in Jordan.Rabbi AvRutick voiced regret that Jews were denied the same privilege in Jordan. He listed various sacred Jewish religious shrines, adding that “no Jew has been permitted to visit the graveside of his parents on the Mount of Olives in old Jerusalem.”
See also here, where the Agudath Israel organization in the US petitioned the UN to allow Jews to visit the Kotel, the Tomb of the Patriarchs, Rachel's Tomb and other holy places.
The Jordanians were zealous in barring Jews from visiting the holy places in the Old City. One amazing example happened in 1959, when a member of Canada's Parliament was not allowed to visit the Old City along with his fellow MPs because he was Jewish:
A member of the Canadian House of Commons was denied permission yesterday by the Jordanian authorities to enter the Jordan-held Old City of Jerusalem to inspect the Holy Places because he was a Jew.Leon D. Crestohl, of Montreal, who is a member of the nine-man Canadian parliamentary delegation currently visiting Israel, was barred by the Jordanians when he sought to accompany the delegation on a tour of the Holy Places. Mr. Crestohl urged his fellow delegation members to make the tour without him.“I am delighted that my colleagues have enjoyed a pilgrimage to the Holy Places,” he said later, “but I am disappointed that I was denied the same privilege to visit the Jewish Holy Places to which all faiths enjoy a recognized form of access according to the armistice agreements.”
Not only was a member of Canada's Parliament banned because he was Jewish, but the government of Canada did not even condemn Jordan's official antisemitism - and neither did Crestohl.
There is only one exception I am aware of, when Jordan allowed Jews to come over for twelve hours in 1957, as I wrote in this post from 2010. Jews who had used to live in the Old City were so loud in their crying over the many destroyed synagogues that is caused an incident and Jordan shut the doors again.
This was state-sanctioned antisemitism, and Jordan made no apologies for it. In fact, it was ready and willing to create international incidents to defend its right to discriminate against Jews.
To think that today's anti-Zionism is any different from the antisemitism that spawned it is just gaslighting.