I heard the Dome of the Rock was built on the site where the Holy of Holies was, and that also it is on the site where the Third Temple will descend from heaven to earth. So will the Dome of the Rock be obliterated when Moshiach comes?
The Rambam at the end of melachim umilchamoseihem says that when Moshiach comes all the muslims and notzrim will realize that their ancetors have been teaching them lies and falsities, and will realize the error of their ways -- and he also says that Moshaich will gather all of th other nations under the one Hashem + Torah etc., so its clar there will be no other religions, from the Rambam, hilchos melach hamashiach (end of melachim umilchamoseihem) -- see there for details, but its all in there.
Also Rashi says in Sukkah that the 3rd temple will descend from shamayim to its original place, so obviously we will also need to make room for the 3rd temple.
So 1) there wil be no other religions besides for the One True Hashem and his Torah AKA Judaism + Noahidism (SEE RAMBAM above for sources on that), so obviously there will not only be no more need for it, but it will be a stumbling block for the masses, and everyone will know its not true etc.
According to our sources Islam will become obsolete because Islam was based on false prophecy as explained here.
Hence there will be no need for it as nobody will be Muslim. The only use would be as a museum, and there's no reason to think that will be the case, especially since this will be prime real estate near or on the Third Temple area.