Question: David why do Jews by birth not see Jews who convert as being fully Jewish?
Answer : Any Jew by birth who sees a Jew who has converted to our people's faith as not being a Jew is speaking utter crap. Once a person has converted to Judaism, i.e. has the approval of a Beth Din, been immersed in a mikveh and if male circumcised (which can be done prior to conversion under General anesthetic by a professional medical practitioner) & is willing to accept the Jewish lifestyle then he or she is fully Jewish. There is no distinction between a Jew from birth and a Jew who has converted. Contrary to popular belief Jews are not a race, but a nation in a perpetual and unbreakable covenant between the Jewish people and God . The Torah is our Constitution and that is the responsibility that a potential convert is taking on. Here is what one of the Rabbinical Midrash says about converts and how loved they are by God :
"Dearer to God than all of the Israelites who stood at Mount Sinai is the convert. Had the Israelites not witnessed the lightning, thunder, and quaking mountain, and had they not heard the sounds of the shofar, they would not have accepted the Torah. But the convert, who did not see or hear any of these things, surrendered to God and accepted the yoke of heaven. Can anyone be dearer to God than such a person".
Lech Lecha 6:32