This statement of Mandatory policy in then Palestine basically adopted the term "status quo" as regards the Western Wall which, at the time, had become an object of dispute as to Jewish rights to it and at it.
As MP Kenworthy stated in Parliament then, there were claims, unaddressed in the White, that Moslem authorities had infringed upon Jewish rights according to custom:
That clipping is from the December 21, 1928 issue of the Palestine Bulletin.
Here is the text of the White Paper as published in the newspaper on December 6, 1928:
As regards the Temple Mount, which wasn't a Jewish demand then but which became the "reason" the 1929 riots broke out in which 133 Jews were murdered by Arabs who thought that Jews were intending to take over the Temple Mount and destroy Al-Aqsa, take note of this 1931 decision published in the Palestine Bulletin on December 14
Today's "status quo", which began in June 1967, ignored the struggle over Jewish rights and, as I have noted, is being fought by the Palestinian Authority who wish to erase entirely even that 1928 status quo.
From Jeffrey Goldberg in The Atlantic:
In September of 1928, a group of Jewish residents of Jerusalem placed a bench in front of the Western Wall of the Temple Mount, for the comfort of elderly worshipers. They also brought with them a wooden partition, to separate the sexes during prayer. Jerusalem’s Muslim leaders treated the introduction of furniture into the alleyway in front of the Wall as a provocation, part of a Jewish conspiracy to slowly take control of the entire Temple Mount.^
Many of the leaders of Palestine’s Muslims believed—or claimed to believe—that Jews had manufactured a set of historical and theological connections to the Western Wall and to the Mount, the site of the al-Aqsa mosque and the Dome of the Rock, in order to advance the Zionist project. This belief defied Muslim history—the Dome of the Rock was built by Jerusalem’s Arab conquerors on the site of the Second Jewish Temple in order to venerate its memory (the site had previously been defiled by Jerusalem’s Christian rulers as a kind of rebuke to Judaism, the despised mother religion of Christianity). Jews themselves consider the Mount itself to be the holiest site in their faith. The Western Wall, a large retaining wall from the Second Temple period, is sacred only by proxy.
The spiritual leader of Palestine’s Muslims, the mufti of Jerusalem, Amin al-Husseini, incited Arabs in Palestine against their Jewish neighbors by arguing that Islam itself was under threat. (Husseini would later become one of Hitler’s most important Muslim allies.) Jews in British-occupied Palestine responded to Muslim invective by demanding more access to the Wall, sometimes holding demonstrations at the holy site. By the next year, violence directed against Jews by their neighbors had become more common: Arab rioters took the lives of 133 Jews that summer; British forces killed 116 Arabs in their attempt to subdue the riots. In Hebron, a devastating pogrom was launched against the city’s ancient Jewish community after Muslim officials distributed fabricated photographs of a damaged Dome of the Rock, and spread the rumor that Jews had attacked the shrine.