Most of us are familiar with the verse from Leviticus:
20:13 If a man also lie with mankind, as he lieth with a woman, both of them have committed an abomination: they shall surely be put to death; their blood shall be upon them.
If you believe that the Torah was dictated by God and you believe in your heart that homosexuality is perfectly moral, then you have a real dilemma. Either God is wrong, you are misreading the verse, or your belief about homosexuals is wrong. Many Rabbis on the bleeding edge of Modern Orthodoxy attempt to argue that it's our understanding of the Torah that's at fault. Because of the clarity of the verse, however, they don't have much wiggle room.
They start with the obvious step: God doesn't have a problem with homosexuals themselves, but only with males having sex with each other. This has the advantage of being a literal reading of the verse, but it isn't very satisfying. Why would God feel so strongly ("an abomination") about an act of love between two people whom God has nothing against?
The Rabbis often proceed to argue that there is no such thing as a homosexual person, only homosexual behavior. The only problem with this argument is that it is clearly untrue.
The more intellectually honest Rabbis recognize that and argue instead that being a homosexual is analogous to being a person with constant urges to commit theft or pedophilia. As long as he doesn't act on his urges, he has done no wrong. This argument seems consistent with the rest of the Torah but it's a retreat to a stance which we cannot reconcile with our modern belief that homosexuality is moral. It's one thing to command people to resist urges which, acted upon, would harm others; it's quite another to command someone to go his whole life without a love-relationship.
A few, unsatisfied with this result, argue that the verse refers only to anal sex, and that other forms of homosexual lovemaking are acceptable. However, this interpretation makes little sense. If we were to extend this logic to the previous verse, should we assume God allows having a relationship with your daughter-in-law, as long as you don't have vaginal or anal sex?
These bleeding-edge Rabbis are by and large good men*. They sympathise with (or in at least one circumstance are) gay men and they are trying to make the reasonable ruling. They are constrained, however, by their inability to make the obviously correct but Orthodoxly-untenable argument about the verse: it was written thousands of years ago by mortals. As a result, many homosexuals from Orthodox families run away from home, develop emotional problems, are ostracised from their families and communities, or commit suicide.
In this way do good men commit evil.
* A note for my readers unfamiliar with Orthodox Judaism: all Orthodox Rabbis are men.
I highly recommend the documentary Trembling Before G-d, which tells the story of Orthodox and formerly-Orthodox homosexuals.