I've noticed that it's hard to find New Church perspectives on homosexuality online so I've decided to provide links to the best articles on the topic that I'm aware of.
To be clear, I'm not interested in starting a debate on this topic. There are other venues for that. I want to provide resources to people who are looking for perspectives on homosexuality from people who believe, to differing degrees, in the theological writings of Emanuel Swedenborg.
Different New Church organizations have different positions on homosexuality. The positions of 3 of the organizations are briefly described in a "List of Christian denominational positions on homosexuality" on Wikipedia.
The majority of the articles here are by members of the General Church of the New Jerusalem. There are also a few articles by members of the Swedenborgian Church of North America. You can find a statement of the position of the General Conference of the New Church in the June 2009 issue of New Church Lifeline (PDF). (I found the PDF hard to read because it's formatted for printing so I copied the relevant portions into this extract.)
I don't have any articles by members of the Lord's New Church which is Nova Hierosalyma, the Church of Truth, the New Church of Southern Africa, or the New Church in Australia. Please let me know if you find any information about these other organizations' positions.
"Homosexuality" by Rev. Jeremy Simons.
Do the Writings talk about homosexuality? Simons, a pastor in the General Church, addresses this question, discusses the various passages that seem to be talking about it, and compares the phrases that Swedenborg seems to use for homosexuality with phrases used by his contemporaries.
"What the Word Says Directly on Homosexuality" by Rev. Grant Odhner.
Odhner, a pastor in the General Church, has collected these notes on homosexuality. They include an overview of how the Old Testament, New Testament, and the Writings treat of homosexuality directly and they also include some thoughts about causes of homosexual feelings and behavior, differing degrees of the seriousness of homosexuality, and some principles from the Writings about how to deal with homosexuals.
"Notes on Homosexuality" by Rev. Mark Pendleton.
In these 18 pages of notes, Pendleton, a General Church pastor, includes passages on love, marriage, adultery, and judging others. He also includes portions of Rev. Jeremy Simons' research and references to a study by Rev. Willard Heinrichs.
"The Worst Adultery" (PDF) by Rev. John Odhner. (New Church Life 1993: 453-463.)
In the explanation of the story of Sodom and Gomorrah (Genesis 19) the phrase "worst form of adultery" is used (Arcana Coelestia 2220). Odhner, a pastor in the General Church, addresses the question of whether homosexuality is the worst form of adultery, in the light of other teachings about adultery.
"A Theology of Sexuality" by Rev. Alain Nicolier - Part 1 (PDF) and Part 2 (PDF) (scroll down to 356-364). (New Church Life 2008: 318-328, 356-364.)
Nicolier, a pastor in the General Church, discusses theories, "myths," and negative influences (particularly from parents) that may cause people to identify themselves as homosexual.
"More on Understanding Homosexuality" by Rev. Grant Odhner. (New Church Canadian Fall 1992.)
This is a letter that Odhner wrote in response to an article by Rev. Glenn Alden, "Understanding Homosexuals," in the February 1992 issue of New Church Canadian. He discusses the theological origins of homosexuality, compares homosexuality with polygamy and concubinage, and ends by discussing human responsibility and repentance. He writes, "in summary, I think we need to see homosexuality as an evil, as something people are ultimately responsible for, as something that can change through sensitive education and repentance."
"Risking on the Side of Compassion" by Rev. James Lawrence. (The Messenger Nov. 1996.)
In this article, Lawrence, a pastor in the Swedenborgian Church, explains why he decided to bless homosexual unions.
"What is True Conjugial Union?" by Duane V. Beougher. (The Messenger Nov. 1996.)
In this response to Lawrence's article, Beougher, a member of the Swedenborgian Church, argues that the Writings are clear that homosexual relations cannot constitute a true conjugial union and that the term marriage should only be applied where that possibility exists.
"Letter to the Editor" by Dr. Reuben P. Bell. (The Messenger Jan. 1997.)
In this letter to the editor in response to Lawrence's article, Bell, a former pastor of the Swedenborgian Church and then the General Church, explains why he sees Lawrence's position to be a profane, dangerous, and harmful abuse of the truth.
"Further Thoughts in Response to Gay Marriage Commentary" by Rev. James Lawrence. (The Messenger June 1997.)
Here Lawrence responds to people's reactions to his article by saying that he does not look to the Writings as the ultimate determinant for his theological position on the nature of homosexuality but instead seeks "a new theological framework" and that he believes that "gay love... is profaned or made sacred by the integrity of the individuals involved."
"Homosexuality" by Rev. Coleman Glenn.
In this blog post, Glenn, a recently ordained pastor in the General Church, explains how it’s possible for someone to think that homosexuality is a disorder and still approach homosexuals with love, and why he thinks of homosexuality in the same way that he think of brother-sister incest. I recommend reading the comments that follow the post.
"Homosexuality" by Brian Smith.
In this blog post, Smith, a theological school student in the General Church, explains why he believes that a person can oppose the practice of homosexuality from love, why he thinks the practice of homosexuality is harmful, and why he seeks to help people who have that struggle see that there is a path out. There is a lot of discussion in the comments that follow the post, mostly between members of the General Church and people who grew up in the General Church but no longer associate themselves with it.
Discussion on BeliefNet
This is a long discussion on BeliefNet of homosexuality from the perspective of Swedenborg's theological works. I read and skimmed the first fifth of the entries. I would guess that the contributors include members of the Swedenborgian Church and General Church and people not affiliated with any organization.
I know that there are other articles and posts that have been written on this topic. (For example, a number of articles come up if you search for homosexuality in New Church Life on HeavenlyDoctrines.org.) If you find an article or post that you think should be included here, leave a comment with a link and a short description of the content of the piece.
UPDATE: Since I first posted this on June 4th 2009 I have received a number of additional articles. I have added a link to an article expressing the position of the General Conference of the New Church, a study and an article by Rev. Grant Odhner, and some notes by Rev. Mark Pendleton.
I have also changed the link for the discussion on BeliefNet. Rev. Jeremy Simons pointed out that only half of the discussion was available at the old link. He recommends the end of the full discussion.