There are different opinions on what will happen to non-Jews when the Moshiach comes.
Some say that they will all convert to Judaism.
As far as the Noahide movement, I suggest the rabim read the Sefer Yisrael v’ haAmim by the gaon, Rav Eliyahu Benamozegh.
He was of the shita that those who fall under the Meiri’s shita would automatically be considered Noahides, since world religions generally are ethical and monotheist (even Hindus affirm the concept of a unified Godhead).