What is the Conservative view of Patrilineal Descent?
In 1983 the Reform movement made an unprecedented break from Jewish law and resolved that "the child of one Jewish parent is under the presumption of Jewish descent". This decision deliberately ran contrary to all previous Jewish law, which has been continuously followed for over two thousand years.
In Jewish law, one is a Jew only if one's mother is Jewish, or if one converts to Judaism. Indeed, one having a Jewish mother is not always sufficient to be considered a full fledged Jew. Specifically, one who has a Jewish mother but is brought up in a another religion is required to go through an educational process and symbolic reentry ritual involving immersion in a mikva before being accepted by the Jewish community as one of their own.
In 1986 the Committee on Jewish Law and Standards (CJLS) approved a Standard of Rabbinic Practice which was overwhelmingly approved at the annual Rabbinical Assembly convention. This reiterated the commitment of the Conservative movement to the traditional Halakha of matrilineal descent, and stated that any rabbi who accepts the principle of patrilineal descent will be subject to expulsion from the Rabbinical Assembly.
To learn more about how this issue affected the entire Jewish community, in all denominations, see:
http://learn.jtsa.edu/topics/reading/bookexc/wertheimer_people/chapter9.shtml