In the United States, the Reform, Reconstructionist, and Conservative movements have all taken official positions in favor of gay rights. Those three movements represent about 80% of affiliated Jews. Of the unaffiliated Jews I think they would overwhelmingly support gay rights as well.
Those three movements all welcome women into their seminaries, so the idea of a rabbi being a man with a long beard is quickly becoming a stereotype of the past.
Rabbi Sharon Kleinbaum is correct, in my opinion, according to my conscience. There is nothing immoral in people forming committed relationships with the person they love, they desire.
A "religious" approach that claims authoritative understanding of a sacred text, claiming that God is the author of that interpretation, is a perversion of religion because it gives individuals an excuse to turn off their conscience.
The story of the Garden of Eden in Genesis comes to teach us that our consciences have been turned on. We were given the ability to distinguish between good and evil. To take that God-given ability and discard it at the directive of some "authority" is, in my opinion, an abomination.
I've written about the abuse of sacred text on my blog and how it serves the human spirit when personal responsibility is affirmed and "authoritative" readings of texts are rejected.
For an elaborate, fun, and deep contemporary interpretation of the Garden of Eden story, read Philip Pullman's "His Dark Materials" trilogy.