It took me just a few minutes of googling to find a huge number of sites referring to Rachel's Tomb or Kever Rachel (the Hebrew name), but hardly any calling the site "Bilal bin Rabah Mosque."
Then yesterday I saw this article on JPOST which provided the most detailed and thorough refutation of the Palestinian claims yet. It really seems that in the case of Rachel's Tomb this is nothing more than a brazen attempt by the Palestinians to co-opt an unquestionably Jewish religious site.
Here's a sample from the JPOST article:
For centuries, Rachel’s Tomb was considered only a Jewish holy place.Read the whole thing.
The 16th-century Arab historian Mujir al-Din regarded Rachel’s Tomb as a Jewish holy place. Beginning in 1841, the keys to the place were deposited exclusively with Jewish caretakers who managed the site until it fell into Jordanian hands in 1948. In contravention of the armistice agreement, Jordan prevented Jews from accessing the site during all the years of its rule (1948-1967).
Following the Six Day War, Jews returned to Rachel’s Tomb, with millions of Jews from around the world having visited the site. According to Jewish tradition, Rachel died on the 11th day of the Hebrew month of Heshvan; in 2010, some 100,000 Jews visited Rachel’s Tomb on that day (October 19).