Our Relationship with Normative Judaism
Unfortunately, because of the aggressive work of Christian missionaries (and of Jews-for-Jesus, Hebrew Christians, Messianic Jews, Nazarenes, etc), mainstream Jews hold any "Jew" who claims a connection with the teachings of Yeshua` of Nazareth with grave suspicion.
The big, big difference between all the above groups and us, is that, while the other groups try to convert Jews to Christianity, we are trying to convert Gentiles (non-Jews) to Judaism / Yahwism.
When a non-Jew comes to us for conversion, they are not specifically converted to Talmidaism, but more generally they are converting to Yahwism - the central religion of ancient Israel, and they are welcomed into the House of Israel.
We see ourselves very much as part of the Jewish tradition. We have the interests and future of the Jewish people very much at heart. Whatever happens to Israel and the Jews of the Diaspora, also happens to us.
What we accept of Yeshua`'s (and his "brother" Ya`aqov's) teachings is social justice, compassion, kindness, forgiveness and mercy. We accept only his complete humanity. To us, he is a Jewish prophet, not a messiah. Our Yeshua` is Jewish. Ask us to choose an allegiance between the Christian community and the Jewish community, we would not hesitate to choose the Jewish community.
Our mission is not to Jews - we don't "convert" Jews because Jews don't need converting - they are already Yahwists. Our mission is on the one hand to convert Gentiles to Yahwism, and on the other to spread the message of the kingdom of God to the nations, and bring ever nearer the day when the nations shall turn to Zion and acknowledge the One-ness of the God of Abraham.
Actually, it is perhaps worth pointing out here that we view Jews who convert to Christianity as Jews who have abandoned their God, and gone after false pagan gods, to pray in "other names".
It is unfortunate that, at the end of the 1st century CE, the Council of Yavneh defined Judaism so tightly, that the beautiful variety and tapestry of Jewish diversity was lost. We were - and are - no threat to our beloved Jewish community. We are a distinctively Jewish sect. We want the unity of the Jewish people - unity in diversity, as it once was before the Second Temple was destroyed.