First and foremost, being gay is not a sin. Having an attraction to members of the same sex does not automatically mean that one is always acting on it in ways the Torah considers an abomination.
Secondly, we are to practice being Dan L’Kaf Zechus, which means we should not automatically assume that someone who is gay is automatically sinning in that way. If, perchance, they stumble, they are no different than those who commit any other sin. We are to be supportive and understand their struggles, as long as they recognize that they are in violation of Halacha and keep their sex lives private.
The question arises: What if these violations are deliberate? What if they go further and make it public, or even proclaim pride in being gay? What if they enter into a same-sex relationship or marriage? Should that be acceptable within the community? What if they are observant in every other way? What if they believe that the Torah’s prohibition does not apply to them as one or two far left rabbis have maintained? The vast majority of Poskim reject that argument outright - considering it beyond ridiculous. But a gay Jewish couple has every incentive to believe it. Should they be accepted as part of the observant Jewish community?
Some may argue that it is no different than accepting someone who openly violates Shabbos. Maybe. But I think that may depend on where they are coming from. If someone was raised in a non observant home or was not educated religiously, we are obligated to accept them and even reach out to them. We should show them the beauty of Judaism, which includes observing Shabbos.
But if someone scoffs at keeping Shabbos and boasts about not keeping it, I’m not so sure we should accept them. On the contrary, we should oust them from the community, preventing them from having any influence on the rest of us. I think the same principle should apply to people who deliberately violate any law of a serious nature. If the violation is flagrant, especially if there is pride associated with it, there should be no more acceptance than for a Jew who is a flagrant and proud idolater.
Let us backtrack a bit. The question is often asked whether a Kohen who is gay should be allowed to Duchen - perform the priestly blessing of the Jewish people assigned strictly to a Kohen by the Torah As it is observed today, it is given every day during Shacharis (morning dervice) in Israel - and outside of Israel, during the Musaf service on religious holidays..
In my view, being gay does not preclude a Kohen from Duchening, especially if we have no way of knowing whether he is acting on his sexual desires. On the other hand, if he deliberately violates this prohibition, he should be considered in the same category as someone who deliberately violates any other Halacha.
It is not, however, entirely clear what that means. Opinions vary on whether someone who violates even Shabbos should be permitted to Duchen. Many Poskim of the highest stature have said that as long as they do not violate any Halachos pertaining to their status as a Kohen, they are permitted to do so. Is being openly gay more of a problem than being an open desecrator of Shabbos? There is much discussion among the Poskim on this topic. The only broadly accepted disqualifier, beyond violating Kohanic laws, seems to be murder.
This question has generated some heated and passionate discussion. Should a rabbi of a Shul prevent an openly gay person from Duchening? My inclination is to say yes. I don't think acceptance of someone that deliberately and flagrantly violates any capital Halacha like Shabbos or the prohibition against gay sex - knowing the serious nature of that violation - should be accepted into the community. On the other hand it seems that a Kohen like that may Duchen. I'm not sure how to reconcile this dichotomy.
New Update:
Rabbi Michael Broyde has written an expansive treatise on the subject of whether a kohen in a same sex relationship may duchen which has not been published in English. They are now available here in Hebrew and here in English.