This article on lesbian, gay, bisexual and transgender clergy in Judaism concerns LGBT people who are open about their sexuality and who are ordained as Jewish clergy (rabbis).
Lionel Blue, who was ordained as a rabbi in 1960, was the first British rabbi to publicly come out as gay.
The ordination of openly LGBT people in Judaism started in 1984 with Reconstructionist Judaism, when the Reconstructionist Rabbinical College, the sole Reconstructionist seminary, voted to accept and ordain rabbis without regard to their sexual orientation.   In 1985 the Reconstructionist Rabbinical College ordained Deborah Brin as the first openly lesbian or gay rabbi in Judaism.
In the late 1980s the primary seminary of the Reform movement, the Hebrew Union College-Jewish Institute of Religion, changed its admission requirements to allow openly lesbian and gay people to join the student body. In 1990, the Union for Reform Judaism announced a national policy declaring lesbian and gay Jews to be full and equal members of the religious community. Its principal body, the Central Conference of American Rabbis (CCAR), officially endorsed a report of their committee on homosexuality and rabbis. They concluded that "all rabbis, regardless of sexual orientation, be accorded the opportunity to fulfill the sacred vocation that they have chosen" and that "all Jews are religiously equal regardless of their sexual orientation."
In 1999 Steven Greenberg publicly came out as gay in an article in the Israeli newspaper Maariv. As he has a rabbinic ordination from the Orthodox rabbinical seminary of Yeshiva University (RIETS), he is generally described as the first openly gay Orthodox Jewish rabbi.  However, some Orthodox Jews, including many rabbis, dispute his being an Orthodox rabbi. 
In 2003 Reuben Zellman became the first openly transgender person accepted to the Hebrew Union College-Jewish Institute of Religion, where he was ordained in 2010. Elliot Kukla, who came out as transgender six months before his ordination in 2006, was the first openly transgender person to be ordained by the Hebrew Union College-Jewish Institute of Religion.
Also in 2006, the Committee on Jewish Law and Standards, the body for Conservative Judaism, adopted two majority opinions, one allowing the ordination of LGBT clergy, as well as the blessing of same-sex unions, and lifting prohibitions on most (but not all) same-sex conduct (specifically not same-sex anal sex) and the other majority opinion retaining traditional opinions. The two primary seminaries for Conservative Judaism, the Jewish Theological Seminary of America and Ziegler School of Rabbinic Studies in response started allowing openly-LGBT students. Also in 2006, Chaya Gusfield and Rabbi Lori Klein became the two first openly lesbian rabbis ordained by the Jewish Renewal movement. They were both ordained at the same time in January 2006.
In 2007 Rabbi Toba Spitzer became the first openly lesbian or gay person chosen to head a rabbinical association in the United States when she was elected president of the Reconstructionist Rabbinical Association at the group's annual convention, held in Scottsdale, Arizona.
In May 2011, Rachel Isaacs became the first openly lesbian rabbi ordained by the Conservative movement’s Jewish Theological Seminary ("JTS"), which occurred in May 2011. She transferred to JTS from the Reform movement’s Hebrew Union College-Jewish Institute of Religion in her third year of rabbinical school.
In 2013, Rabbi Jason Klein became the first openly gay man chosen to head a national rabbinical association of one of the major Jewish denominations in the United States when he was elected president of the Reconstructionist Rabbinical Association at the group’s annual convention, held in New Orleans. 
Together, Reconstructionist Judaism, Reform Judaism, and Conservative Judaism make up 75% of Jewish Americans who belong to a synagogue.  The remainder of synagogue-belonging Jews belong to either Orthodox Judaism, at 21%, who do not ordain openly LGBT Jews, and a remaining 4% belonging to either an unaffiliated synagogue or another Jewish denomination which may or may not ordain openly LGBT Jews.
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