There is no Jewish world consensus as to what a Jew actually is. The State of Israel has one definition. Reform ("liberal") Judaism has another. Orthodox Judaism has a third. There are those within each group who think of their Judaism as a culture, or a race, or a religion, or a mixture of all. The closest thing to a statement of faith they have is Maimonides' Thirteen Points, and not even all agree to that. There are agnostic, communistic, and religious Jews. It's even permissible to not believe in God at all, but the one thing that they're in consensus about is that a Jew cannot be a Christian. For a Jew to call upon Jesus as Savior, Lord or Messiah, makes him a non-Jew in all the major Jewish communities and branches. "Messianic" Judaism is not accepted as an alternative form of their faith. At the time when the N.T. was written, this was not the problem that it is today. But in AD 90 the synagogues at the Council of Jamnia (or "Jabneh") in Roman Palestine declared all Jews who believed in Christ as heretics and "non-Jews". And this prejudice has remained until today. Yet if you read the rest of Romans 11 and Romans 1:16, the text anticipates this Jewish rejection of Jesus, yet it still puts a priority on Jewish mission work.
2. The rabbis teach that no Jew who accepts Christ has truly understood his own religion. Yet the history of Jewish conversions will refute this.
The facts of history negate it. Take Rabbi Isaac Lichtenstein for example: a Hungarian Orthodox rabbi of the 19th Century who one day found a New Testament, took it home, read it in anger, and left it alone on his shelf for 30 years. But one day during a pogrom in his district (a government or church-organized riot against Jews), he wondered why Christians were so angry at his people. So then he read it. "I looked for thorns, and gathered roses," he said later. "The half has not been told to me of the greatness, power and glory of this book, which was sealed to me at one time." Gradually he began to use New Testament material in his pulpit preaching until one day he confessed his belief that Jesus was the Jewish messiah and astounded the Jews of Hungary. When called before the Chief Rabbi of Budapest to recant, he refused to do so. His fellow-rabbis demanded that he resign, but his own congregation allowed him to stay as their rabbi until he himself finally resigned. Yet he continued his writing and visitation gospel ministry across Europe.
And there were others: very knowledgeable in the faith of their birth: Joseph Wolff for example: his father a rabbi, born in Bavaria in 1795, ordained as an Anglican missionary, he preached the gospel in Palestine and throughout the Middle-East. And Samuel Schereschewski: one of the greatest Orientalist linguists of the 19th Century, Episcopal bishop to China, he translated the Hebrew Scriptures into two separate Chinese languages. And August Neander, called the "Father of Modern Church History", born in Germany in 1789, studied at the University of Halle and was encouraged by classmates to examine the messianic claims of Jesus including Isaiah 53, a student of Friedrich Schleiermacher (a.k.a. "The Father of Theological Modernism"), who refuted his former professor and showed the validity of Scripture against the tide of Schleiermacher's Higher Criticism.
3. Jewish religious schools teach their children an aspect of church history that Christian religious schools never teach their children.
By the time most Jewish boys and girls reach the age of Bar-Mitzah (or Bat-Mitzvah) they know about the pogroms, the Crusader massacres of Jewish communities, the blood libels, the Spanish Inquisition, the Church-sponsored expulsions of Jews from almost every country in Europe, and the Holocaust. And in each case, aside from the Holocaust, they're taught that the major persecutor was the Church. The irony is ... they're correct: The organized, visible Church with all its problems and bigotries, indeed did those things. But what they're not taught is that those same churches were persecutors of true Christians too. But while the persecuted continued to worship God more fervently, the Jews used that persecution as their excuse to continue to reject to Gospel.
4. Mission work among Jews yields small numbers of converts, yet Scripture promises a blessing to the Church for doing it.
If a church is solely focused on numbers of converts as a gauge to decide how to allocate resources, it misses the point of Jewish evangelism, Read Romans 11: 11 and 15. Regardless of what you think this text is saying, and granted, that text creates more questions than it answers, notice at least this: it's saying that since their rejection of Christ meant blessing for the nations, then their conversion to Him will yield blessings more abundant. Verse 15 is a parallel passage to verse 11. (It's saying the same thing.) And Paul wrote this after he had been commissioned as an apostle to the Gentles. He was saying that though the Jews were no longer his primary mission field; still, that blessing about their inclusion into the fold of Christ remains. Christians can debate the "whys" of this question endlessly, yet the statement still stands as true, according to Paul.