Idolatry and the building of the third Temple

When the third Temple is built, what will happen to the churches and mosques that populate the Holy Land especially Yirushalaim? Also, since the whole world will recognise Hashem as the one G-d, will it be the case that all other religions will be no more? Thanks

The question is indeed interesting. There may be sources to suggest one forecast or another, but I personally refer to the Rambam at the end of Mishna Torah in these matters, who says that no one knows what it will be like until it happens. Source material on this topic may be found in the first 3 pages of tractate Ovoda Zora, Last chapter of Sanhedrin and Sotah. But still a quote from the Talmud is not enough to formulate an ironclad belief in specific events and global, social and religious phenomenon during the days of Mashiach. May we know the answer to this question soon in our day.