There is no one single Jewish perspective on other religions. The tradition has produced a wide spectrum of views, ranging from warmly accepting to egregiously intolerant.
It is likely unsurprising that, historically, those views of non-Jews and their religions which are least tolerant generally have been produced by Jews who were experiencing oppression by non-Jews at the time. The most accepting and tolerant views tend to be modern, coming from Jews in places where Judaism is tolerated and Jews fare well in society.
That said, there are always exceptions. Some of the Rabbis of the Talmud, who certainly had no reason to feel warmly toward non-Jews, being themselves oppressed by the Romans, nonetheless differed from their Rabbinic colleagues who vituperated the non-Jew and instead taught that justice and righteousness could come from all quarters, not just from one's fellow Jews. And likewise, today, there are some among the Ultra-Orthodox who, despite living in America and enjoying unprecedented freedom and toleration, nonetheless dismiss non-Jews as soulless and animalistic, and their religious practices little better than demonolatrous excess.
Of course, much of that is fringe opinion, also. Within the main stream, the tendency historically has been to be cautiously accepting of non-Jews but unaccepting of their religious practices. The classical halakhists (legal scholars) usually more or less taught that Christians and Muslims, being monotheists, were merely in serious error about their religion, but there was no reason they could not be decent people, provided that they behaved well. Some taught that prolonged exposure to such error degraded the soul, though. And few had much tolerance for polytheists. Judaism has seldom had much tolerance for polytheism and the use of idols in worship. Some (but by no means all) of the Kabbalists had very intolerant opinions of non-Jews and their religions indeed, and these ideas got picked up by certain authors in the mussar (moralistic philosophy) movement, resulting in some rather unsavory teachings which persist in some Jewish communities even unto this day.
Today, what you will usually find is that nearly all non-Orthodox Jews and most Modern Orthodox Jews will be tolerant, if not accepting, of non-Jewish religions. There is a lot of effort made, especially in the non-Orthodox communities, to find pluralistic theology, and to see non-Jewish religion as ways in which God has chosen to relate to other peoples, potential other covenants with different traditions. Interfaith dialogue is embraced, and many try to find the beauty or insight into the ways that other traditions have experienced the divine and the Creation.
There is even some conscious embracing of syncretism in non-Orthodoxy, mostly from Buddhism and Taoism, which in their purest forms are not really religions so much as philosophies of life, but also from other sources, including such unlikely sources as Hinduism and Islam. This is especially true in the Jewish Renewal movement, but sometimes works its way into Reform or Conservative Judaism. Syncretic assimilation from Christianity is generally universally avoided in philosophy and theology, but is sometimes accepted in relation to liturgical styles, summer camp programs, rehabilitation programs, prayer service practices, and rabbinical preaching styles. This is especially true in the Reform movement, which has historically always been syncretic with Protestant practices.
Mainstream Orthodoxy is far less tolerant. In general (though there are exceptions), the prevailing spectrum of opinions in Orthodoxy range from the "accept the people, disdain the religion" view to "tolerate the people, abhor the religion" all the way to the "debased, soulless evil worshippers" view. Although this latter is mostly found in Ultra-Orthodox communities, which are fundamentalist in the extreme, and quite insular.
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