Someone pointed out to me that the drafters of that Statement never included any Torah sources to support their document. I agree that this was a mistake on their part, and so I took a few minutes on Friday to assemble some material they could have included. That material is below, as footnotes to the original document.
Please note that I was not a drafter of that Statement, and I do not speak for them. [I did sign, but my own concerns with the document appear here.]
Statement of Principles on the Place of Jews with a Homosexual Orientation in Our Community
We, the undersigned Orthodox rabbis, rashei yeshiva, ramim, Jewish educators and communal leaders affirm the following principles with regard to the place of Jews with a homosexual orientation in our community:
1. All human beings are created in the image of God and deserve to be treated with dignity and respect (kevod haberiyot). Every Jew is obligated to fulfill the entire range of mitzvot between person and person in relation to persons who are homosexual or have feelings of same sex attraction. Embarrassing, harassing or demeaning someone with a homosexual orientation or same-sex attraction is a violation of Torah prohibitions that embody the deepest values of Judaism.
2. The question of whether sexual orientation is primarily genetic, or rather environmentally generated, is irrelevant to our obligation to treat human beings with same-sex attractions and orientations with dignity and respect. 
3. Halakhah sees heterosexual marriage as the ideal model and sole legitimate outlet for human sexual expression. The sensitivity and understanding we properly express for human beings with other sexual orientations does not diminish our commitment to that principle.
4. Halakhic Judaism views all male and female same-sex sexual interactions as prohibited. The question of whether sexual orientation is primarily genetic, or rather environmentally generated, is irrelevant to this prohibition. While halakha categorizes various homosexual acts with different degrees of severity and opprobrium, including toeivah, this does not in any way imply that lesser acts are permitted. But it is critical to emphasize that halakha only prohibits homosexual acts; it does not prohibit orientation or feelings of same-sex attraction, and nothing in the Torah devalues the human beings who struggle with them. (We do not here address the issue of hirhurei aveirah, a halakhic category that goes beyond mere feelings and applies to all forms of sexuality and requires precise halakhic definition.)
5. Whatever the origin or cause of homosexual orientation, many individuals believe that for most people this orientation cannot be changed. Others believe that for most people it is a matter of free will. Similarly, while some mental health professionals and rabbis in the community strongly believe in the efficacy of “change therapies”, most of the mental health community, many rabbis, and most people with a homosexual orientation feel that some of these therapies are either ineffective or potentially damaging psychologically for many patients.
We affirm the religious right of those with a homosexual orientation to reject therapeutic approaches they reasonably see as useless or dangerous. 
6. Jews with a homosexual orientation who live in the Orthodox community confront serious emotional, communal and psychological challenges that cause them and their families great pain and suffering. For example, homosexual orientation may greatly increase the risk of suicide among teenagers in our community. Rabbis and communities need to be sensitive and empathetic to that reality. Rabbis and mental health professionals must provide responsible and ethical assistance to congregants and clients dealing with those human challenges.
7. Jews struggling to live their lives in accordance with halakhic values need and deserve our support. Accordingly, we believe that the decision as to whether to be open about one's sexual orientation should be left to such individuals, who should consider their own needs and those of the community. We are opposed on ethical and moral grounds to both the “outing” of individuals who want to remain private and to coercing those who desire to be open about their orientation to keep it hidden.
8. Accordingly, Jews with homosexual orientations or same sex-attractions should be welcomed as full members of the synagogue and school community. As appropriate with regard to gender and lineage, they should participate and count ritually, be eligible for ritual synagogue honors, and generally be treated in the same fashion and under the same halakhic and hashkafic framework as any other member of the synagogue they join. Conversely, they must accept and fulfill all the responsibilities of such membership, including those generated by communal norms or broad Jewish principles that go beyond formal halakha.
We do not here address what synagogues should do about accepting members who are openly practicing homosexuals and/or living with a same-sex partner. Each synagogue together with its rabbi must establish its own standard with
regard to membership for open violators of halakha. Those standards should be applied fairly and objectively.
9. Halakha articulates very exacting criteria and standards of eligibility for particular religious offices, such as officially appointed cantor during the year or baal tefillah on the High Holidays. Among the most important of those criteria is that the entire congregation must be fully comfortable with having that person serve as its representative. This legitimately prevents even the most admirable individuals, who are otherwise perfectly fit halakhically, from serving in those roles. It is the responsibility of the lay and rabbinic leadership in each individual community to determine eligibility for those offices in line with those principles, the importance of maintaining communal harmony, and the unique context of its community culture.
10. Jews with a homosexual orientation or same sex attraction, even if they engage in same sex interactions, should be encouraged to fulfill mitzvot to the best of their ability. All Jews are challenged to fulfill mitzvot to the best of their ability, and the attitude of “all or nothing” was not the traditional approach adopted by the majority of halakhic thinkers and poskim throughout the ages.
11. Halakhic Judaism cannot give its blessing and imprimatur to Jewish religious same-sex commitment ceremonies and weddings, and halakhic values proscribe individuals and communities from encouraging practices that grant religious legitimacy to gay marriage and couplehood. But communities should display sensitivity, acceptance and full embrace of the adopted or biological children of homosexually active Jews in the synagogue and school setting, and we encourage parents and family of homosexually partnered Jews to make every effort to maintain harmonious family relations and connections.
12. Jews who have an exclusively homosexual orientation should, under most circumstances, not be encouraged to marry someone of the other gender, as this can lead to great tragedy, unrequited love, shame, dishonesty and ruined
lives. They should be directed to contribute to Jewish and general society in other meaningful ways. Any such person who is planning to marry someone of the opposite gender is halakhically and ethically required to fully inform his or her potential spouse of their sexual orientation. 
We hope and pray that by sharing these thoughts we will help the Orthodox community to fully live out its commitment to the principles and values of Torah and Halakha as practiced and cherished by the children of Abraham, who our sages teach us are recognized by the qualities of being rahamanim (merciful), bayshanim (modest), and gomelei hasadim
engaging in acts of loving-kindness).
 Bereishit 1:27. Note Rashi’s alternative translation, which does not reduce the essential force of the sentence.
 The principle of kvod habriyyos appears throughout halachah, with a simple example in Berachos 19b. Ramban in haEmunah v’haBitachon Perek 19 explicitly links it to tzelem Elokim, in a unique way.
 See, for example, Rambam Lo Taaseh 251. So far as I am aware, there is no basis for distinguishing between Jews who desire to sin and Jews who do not desire to sin, in this regard. Just the opposite, Rashi to Yoma 29a הרהורי indicates that we should feel greater sympathy for someone who has a desire to sin in sexual matters, for this weakens his body.
 See note 3. Also, see Succah 52a-b, which points out the involuntary nature of the Yetzer haRa, in general.
 See Vayyikra 18:22-23, for example.
 See, for example, the conduct of Aharon haKohen toward sinners, as recorded in Avos d’Rabbi Nasan 1:12. Surely no one would suspect that Aharon was legitimizing the sinner’s transgressions.
 See footnote 5 re: male relations, and Sifra to Acharei Mot 9 for a fuller presentation.
 Desire for sin does not remove the prohibition; see Sanhedrin 75a, for example.
 As evidenced in the praise of Yosef haTzaddik on Sotah 36b, for the fact that he avoided sin despite great temptation.
 See, for example, Reparative Therapy: The Adolescent, the Psych Nurse, and the Issues, Journal of Child & Adolescent Psychiatric Nursing, February 1, 2010
 Treatments which are viewed medically as dangerous are clearly prohibited under Devarim 4:15. The issue of treatments viewed as useless is more complex, but as a general rule a רפואה שאינה בדוקה carries little halachic weight; see, for example, Yabia Omer 8:Orach Chaim 37. See also Chazon Ish Emunah uBitachon 2:6, in which he condemns hishtadlus through avenues with little chance of success.
 See, for example, Homosexuality as a risk factor for depression and suicidality among men. Facts and ignorance of facts. European Psychiatry; Jan2010 Supplement 1, Vol. 25, p136
 See, for example, Rav Y. D. Soloveitchik’s citation of Rav Chaim Brisker: “However, the main role of the rabbi is to help the needy, protect the persecuted, defend the widows, and sustain orphans. In a word, it is acts of loving-kindness [gemilat hasadim].” (The World of Rabbi Joseph B. Soloveitchik, 193)
 Regarding people who desire to sin and do not sin, and who wish not to be “outed” for those desires, their protection should be obvious. However, such protection even applies to people who have transgressed; see Bava Metzia 59a. Where there is a significant practical reason to disclose their status, the justification of תועלת would likely mandate such reporting.
 Choosing to be public with one’s desires is complex, as it involves the possibility of drawing others into sin; see, for example, Rama Even ha’Ezer 21:5 against public displays of permissible affection, lest that arouse others. Choosing to reveal one’s actual sins is still more complex; see conflicting statements in Berachot 34b and Yoma 86b and Mishneh Torah, Hilchot Teshuvah 2:5, for starters.
 Note the emphasis on those experiencing attractions, not those who have sinned. Regarding those who have actually sinned, see Shulchan Aruch Orach Chaim 55:11 and nosei kelim there.
 See Shulchan Aruch Orach Chaim 53.
 See, for example, Rambam’s Iggeret Teiman (Boaz Cohen translation): Let no man conclude that he may freely disregard the less important ceremonies without liability to penalty because he has committed under duress some major sins.
 See, for example, the Sifra cited in footnote 7 above.
 See Pischei Teshuvah Yoreh Deah 268:10, citing Rashbash, on the importance of accepting even the children of mumarim, much less the children being raised by people who believe in Torah. Further, see Minchas Yitzchak 3:98, Mishpitei Uziel 2: Yoreh Deah 62, Pizkei Uziel 65 and Yachel Yisrael 2 in favor of enrolling the children of Jewish mothers and non-Jewish fathers in Jewish schoools. See also Sridei Eish 2:57, who even favors enrolling of children of Jewish fathers and non-Jewish mothers, pending a possible future conversion. See also Igros Moshe Orach Chaim 2:73, which is more ambiguous.
 See, for example, Husbands who Love Men, Dr. Eileen Atwood
 This would seem to apply where the husband is incapable of conceiving a child with his wife, based upon Kesuvos 77a.