This may sound strange to both Christians and Jews, but it is not proper to consider Judaism and Christianity as separate religions.
In the first ten years after Jesus resurrected, the only believers in him were, in fact, Jews. Even after non-Jews were accepted into the faith by virtue of Peter's vision (Acts 10), first century Christians (Jews and non-Jews) considered Christianity to be a sect of Judaism. Many Christian pundits today make the false claim that it was God's will for the church to move away from everything (instead of only some things) we call Jewish. In the process of tossing out Jewish traditions, Christendom tossed out some jewels of Judaism it should have retained - things like the celebration of Passover, which was, among other things, an idea of God and not men.
Therefore, to the believing Jew, Christianity should be considered a more-correct, or completed form of Judaism; and to Gentiles, a new religion. This is how every author in the New Testament saw it. Or else, why did Paul take part in Jewish purification rites to prove there was nothing to the rumors that he was teaching people to apostatize from the Jewish Torah (Acts 21:17-26)? Or, why does James mention worship in synagogues for Christians in James 2:2, (most English translations don't use the word synagogue here, but that is the very word used in the Greek texts, which is the same Greek word used for the other 46 references to synagogues the rest of the NT).
So, it's important to recognize that non-believing Jews today don't pray to a different God than Christians do. It is not like the difference between Allah for the Muslims and the LORD for Christians. Jews pray to the God who sent Moses, which is also the same God who sent Jesus.
Christian pundits of today will say the vast expanse between Judaism and Christianity happened as a natural course of action based on the writing of the NT. This is not the case. The view of Christianity being merely another sect of Judaism changed in the third century when the Roman Emperor Constantine embraced Christianity as a theocracy and began to Christianize the Roman Empire. Political motives sought to eschew the Jews (even the believing Jews) because there was a very antisemitic atmosphere in Rome. So in order to make Christianity more palatable for the average citizen, Roman leadership "sanitized" Christianity by stripping it of all things Jewish: The Sabbath moved to Sunday and Passover, Pentecost, The Feast of Tabernacles, The Day of Atonement were all stripped and forbidden from Christianity - and these are events that Jesus himself celebrated and used to teach his disciples about God and himself. In fact, the NT says these things are the very shadow of Jesus himself. Why did we toss them if there is so much about them that tells us about who God is?
Here's my point. If we are serious about being credible witnesses to Jewish people (who the Gospel was meant for first, according to Rom. 1:16), then we had better provide a more favorable understanding of Christianity to them. As it is now, to the Jew, Christianity looks like a pagan religion. And when we use the word "conversion" for a Jew who becomes a believer, it has a horrible ring of dropping one religion and embracing a different one, when instead, it should be considered a commitment that leads to the Jew accepting an updated version of Judaism, and an ushering in of more books in his Torah.
