The afternoon Torah reading on Yom Kippur is from Leviticus 18, the passage of forbidden relations. Included in this list is adultery, incest and homosexual relations. Why do we read it on Yom Kippur?
Rashi (Megillah 31a sv. korin ba-arayos) writes that it is to remind anyone who has committed these common sins that they are forbidden and to lead them to repent. Tosafos (ibid., sv. be-minchah) explain that we read this passage because women dress up in their best clothes in honor of the holy day, and men need to be reminded to keep their desires under control. Regardless, the message is clear. These relations are forbidden and we need to remember that and heed the warning.
Steve Greenberg, the "gay orthodox rabbi", has a different take on this (link). He says that, first of all, it is better to read the passage than to deny that it exists. Furthermore:
Second, reading Leviticus 18:22 in shul on Yom Kippur makes gay people present in a powerful, if challenging way. With the proper acknowledgement, the reading can become a call to greater empathy and understanding. We can use it to bring to communal memory the countless people throughout the ages, who, on the most holy day of the year, had no voice in the face the most devastating misrepresentation of their hearts. And lastly, it can serve as an impetus for learning and reinterpretation of the biblical and rabbinic texts that should no longer be a source of self-loathing or exclusion.This is an incredibly self-serving distortion of the Jewish tradition. Should adulterers and those guilty of incest also take the opportunity as "an impetus for learning and reinterpretation of the biblical and rabbinic texts"? I see this idea as being similar to encouraging using the Torah reading of Parashas Zakhor (which teaches us to destroy the memory of Amalek) as a way of embracing Amalek. Or of blowing the shofar as a way of leading us all to sin. Or lighting the menorah as a way of stimulating assimilation and abandonment of Jewish heritage, a common but widely disparaged activity.
Perhaps a better message of the Yom Kippur afternoon Torah reading to the homosexual community is that their desires are as equally strong as heterosexual desires, which is why the Torah lists all of the forbidden relations together. This is their opportunity to shine and to represent the Jewish people in upholding this prohibition despite their strong desires.