The Temple Mount was turned over to the Waqf not because of the ‘leftist West’, but because the socialist establishment in Israel wanted to stamp out any Messianic hopes that might sweep through the Jews of the world.
Defense Minister Moshe Dayan actually undercut Israeli PM Levi Eshkol in immediately ceding the Temple Mount (one of “the Holy Places of others”) to the Jordanian Waqf.
http://www.sixdaywar.org/content/ReunificationJerusalem.asp
For insight into the issues involved in reestablishing Jewish sovereignty on the Temple Mount, see:
http://jcpa.org/jpsr/s99-yc.htm
I did not say it was “because of the ‘leftist West’”. Take note though of the internationalist outlook of socialists, who really do not recognize national borders (this being one source of the left’s antipathy towards having a Jewish state in particular).