A complete account of Peter Danzig's experience can be found on the Equalitysblog
Both individuals were once members of the Church in good standing. Peter went on a mission, married in the temple, composed pieces for Mormon pageants, and taught hymns to children. He and his wife, Mary, also a returned missionary, were raising their three daughters in Levan, but driving to Salt Lake City each week to play in the LDS Orchestra at Temple Square - he on viola, she, the violin. Both believed their music was their gift to God.
However, Danzig began to be concerned about the possibility of excessive censorship on the part of Church leadership, beginning in 1993 when church officials charged six well-known Mormon scholars and intellectuals with apostasy for their writings. His concern grew when Brigham Young University fired history professor Steven Epperson, a member of Danzig's own ward, for serving the homeless instead of attending church.
However, when BYU adjunct professor Jeffrey Nielsen lost his job for arguing in a 2006 Salt Lake Tribune column that the LDS Church was wrong to oppose gay marriage and to enlist Mormon support for a constitutional amendment against it, and Nielsen was fired from BYU as a result, Peter Danzig had reached his limit, and wrote a letter to the editor of the Salt Lake Tribune, expressing his disagreement. Here's the letter, originally published on June 14th, 2006:
As a member of the LDS Church, returned missionary and member of the Orchestra at Temple Square, I am appalled at the intellectual tyranny that our leadership has exercised through the summary dismissal of Jeffrey Nielsen from his teaching position at Brigham Young University for speaking his mind in an op-ed published June 4th  in The Tribune. I was troubled that my church requested that I violate my own conscience to write in support of an amendment (marriage) I feel is contrary to the Constitution and to the gospel of Christ.
I am even more discouraged to see how they deal with an honest difference of opinion.
I wish to express to Jeffrey Nielsen that I admire his courage and that I stand with him. I hope that rank-and-file members of the church as well as members of the lay clergy who also find this troubling will have the courage to step forward and let themselves be known. To do anything else would be to hide in the shadow of an injustice.
The reason I've highlighted the first sentence and a half in red will be forthcoming. Within a week after publication of the letter, LDS officials contacted Danzig with concerns about the letter. It began with a call from Michael Watson, secretary to the church's governing First Presidency, to Barry Anderson, orchestra administrator, and Mac Christensen, president of the Tabernacle Choir, which is associated with the orchestra. Eventually, the Danzigs' stake president and bishop in Levan got involved. Ultimately, the Church suspended him from the orchestra and for the next year, he and his wife defended their loyalty, faith and actions. No amount of persuasion or pleading could convince these ecclesiastical leaders they meant well. Finally, the Danzigs moved out of their Levan house and, in December 2007, resigned their membership in The Church of Jesus Christ of Latter-day Saints rather than face excommunication.
A Church spokesman responded. "There is room in the [LDS] Church for honest disagreement regarding church positions," LDS Spokesman Scott Trotter said. "Disagreement on doctrine only becomes an issue when a church member acts in open opposition to the church or its leaders." None of the other Church officials involved would comment. But deciding when a person is in "open opposition" sometimes varies among Mormon bishops and stake presidents. Clearly, someone at the top thought Danzig had crossed that line. The LDS Church has now published a more formal response on their official website.
While Peter Danzig regrets his syntax, he reaffirms his intent. "In hindsight I could have used some different language, but what I wrote expressed the feelings of my heart," he said. "I have seen the church abuse too many, including my family, without anyone daring to speak out. It is important to me that the silence about this abuse end."
Ironically, between June 2006 and December 2007, the LDS Church came out with several statements acknowledging homosexuality may be inborn and difficult to change, even with much effort and prayer, which is was exactly the position Danzig had been defending.
When asked to comment on this story, Jeffrey Nielsen, who now teaches at Utah Valley State College and Westminster College, said that many committed Mormons, including philosophers, psychologists and some politicians, disagree with the church on the Federal Marriage Amendment. Several other Church members wrote letters to the Tribune defending Nielsen and sharing his view. But Nielsen is unaware of disciplinary action taken against any of those letter writers. A June 2006 story published by the Deseret Morning News better describes Nielsen's termination from BYU.
Another LDS Brigham Young professor who was censored was Steven E. Jones, who was gently kicked to the curb in 2006 for presenting evidence disputing the official cock-and-bull story about 9-11.
Commentary: If you look back at Danzig's letter, you can see the problem, highlighted in red. He identified himself as a Church member and identified his Church position. Had he not included that information, I believe he'd still be a member today, and playing in the orchestra.
The Church simply will not tolerate members taking public positions in opposition to their doctrine, identifying themselves as Mormons, and using public forums to lobby the Church to change policy. This is how I've always understood the policy. The Church is not a democracy - members can disagree without penalty, but when disagreement crosses the line into open dissension or "rebellion", the Church must act. Danzig was offered an opportunity to recant without penalty by writing a letter of apology to the General Authorities, but he chose not to exercise that option.
However, the Church would be wise to ensure that understanding of this policy and its definition are common throughout the ranks and that it is enforced with horizontal consistency. One should not be more subject to discipline simply because his bishop wakes up on the wrong side of bed or his temple garments are pinching his waist too tightly. In addition, the Church shouldn't drag the process out. If they decide to levy discipline, do so promptly. Don't put people through a protracted process. The purpose of Church discipline is to preserve order and harmony within the ranks and not to single out people as examples. The three authorized forms of Church discipline remain probation, disfellowshipment, and excommunication.
Since the Danzigs left voluntarily and were never formally disciplined, it should be relatively easy for them to regain membership if they change their mind about the Church in the future. Being reinstated after an excommunication is much tougher.