Undoubtedly, Judaism- though not proselytizing our beliefs - does accept Converts and Jews are commanded to love and respect the convert. What would happen if the Jewish people, over time, became completely non ethnic Jewish. Meaning descendants of converts - or converts themselves.
What Halachic implications would that have? Would having no more Kohanim, male descendants of Aharon Hakohen, preclude the coming of Moshiach?
Would building the Beis Hamikdash become moot?