Do Jews accept that Jesus Christ came as a man, suffered, and died on the cross?
Historically, there was certainly a man named Yeishu, a Jew, who lived towards the end of the Second Temple era, and died at the hands of the Romans. He is mentioned in the Talmud, and in other Jewish sources. I do not know how much he did or did not suffer, or the significance thereof.
The various facts of Yeishu’s life are accepted by Jews, and, in fact, some of the most profound research on his life has been conducted by Jewish (mostly Orthodox) scholars at the Hebrew University (such as Prof. Flusser, Safarai, and others). Their Jewish background enables them to compare the life and teachings of Yeishu to those of other Tanaitic Sages of the same era, yielding fascinating discoveries.
[It should be noted that there is virtually no scholar today that claims that Yeishu was not a practicing Jew, who kept all the precepts of the Torah. Only Paul, and later disciples, saw it right to ‘abolish’ the law, so to speak, and substitute it with faith alone.]
Further to the basic difference between Judaism and Christianity concerning belief in Yeishu as a God-figure, a fundamental difference between the two is the role of humanity in bringing about the destiny of the world. According to Christian doctrine, after the Fall of the Original Sin, man is doomed to evil, and is totally helpless in mending himself and his world. He should shun the flawed physical world, and await salvation at the hands of God (and His messenger).
According to Jewish doctrine, the precise opposite is the truth. We, too, await the Messiah, but we wait actively, believing that our deeds, in the performance of the holy Torah, are those that mend us and the world, and draw the Messianic Era into the world. Rather than separating, to the greatest possible degree, from the world, we actively engage the world in all ways, brining Divine holiness into the world by applying to it the precepts of Torah.
Thus, even in messianic theology, the difference between the religions is not merely whether the Messiah is coming for the first or second time, but far deeper. Jews contend that belief in the Messiah by definition means belief in our ability to become worthy of the messiah. Christians, on the other hand, argue that belief in the messiah by definition means belief in our inability to become worthy of the messiah, in our needing the messiah to take our sins upon himself. For Christians, the coming of the messiah makes repentance possible; for Jews, repentance makes the messiah possible.
Perhaps the most radical manifestation of this difference is in the area of sexual relations. Christian doctrine (especially Paul) teaches that celibacy is the ideal, and marriage is only the least of evil: “if they cannot contain, let them marry: For it is better to marry than to burn.” Sexual relations could never free themselves from the tarnish that was attached to it, as well as to everything else that was of the body, in Christian thought, and the result, in the twentieth century, was the sexual revolution. The world revolted against the Christian denigration of the human body, and the Christian approach to sexuality, and abandoned a religion that was seen as suppressive and out of touch with humanity.
In Judaism, the Christian sexual ethics entirely misses the point. Judaism teaches that there is a moral and religious obligation to wed a wife. The purpose of this is not only to beget children, but to complete onself as a person (see Tur, Even Ha’ezer 1). Sexual relations are not, Heaven forbid, evil or negative. This would be true only in the context of promiscuous sexual behavior, in which a person sees his physical actions as being on a par with those of animals. In the Jewish tradition, however, even the physical is specifically human, and not animalistic; it has the potential for holiness. Thus, in the context of the marital covenant, sexual relations become an elevated manifestation of holiness and purity.
God desires life, as the verse states, “Life is His will.” And life means not only a soul, but the combination of a body and a soul–a soul that is able to make an impact in this world by means of the body it occupies. Divine purpose thus seeks its realization though human deeds, and we, the Jews, see ourselves as responsible for performing those deeds.