FAIR is a non-profit organization dedicated to providing well-documented answers to criticisms of the doctrine, practice, and history of The Church of Jesus Christ of Latter-day Saints.
Mormonismo e Assuntos Raciais/Negros e do sacerdócio/A pressão social
Social pressure was actually on the decline after the Civil Rights movement and coordinated protests at BYU athletic events ceased in 1971
Jan Shipps, a Methodist scholar and celebrated scholar of Mormon history and culture, considers it factual that "this revelation came in the context of worldwide evangelism rather than domestic politics or American social and cultural circumstances." She wrote:
A revelation in Mormondom rarely comes as a bolt from the blue; the process involves asking questions and getting answers. The occasion of questioning has to be considered, and it must be recalled that while questions about priesthood and the black man may have been asked, an answer was not forthcoming in the ‘60s when the church was under pressure about the matter from without, nor in the early ‘70s when liberal Latter-day Saints agitated the issue from within. The inspiration which led President Kimball and his counselors to spend many hours in the Upper Room of the Temple pleading long and earnestly for divine guidance did not stem from a messy situation with blacks picketing the church’s annual conference in Salt Lake City, but was "the expansion of the work of the Lord over the earth." 
Pergunta: É verdade que o Presidente Jimmy Carter ameaçou o status de isenção de impostos da Igreja por causa da diretriz a respeito do Sacerdócio aos negros?
President Carter had a brief minute meeting with President Kimball, Representative Gunn McKay, and Representative Jim Santini on 11 March 1977 at the White House
On March 11, 1977 at 12:03 pm President Carter met with Spencer W. Kimball, President of the Church of Jesus Christ of Latter-day Saints, Representative Gunn McKay (D-Utah), and Representative Jim Santini (D-Nevada) for approximately 20 minutes in the White House. This meeting, noted in President Carter's White House diary, is popularly rumored among ex-Mormons to be the meeting in which Carter threatened the Church with a rescinding of the Church's tax-exempt status over the issue of the priesthood ban.
President Carter visited Salt Lake City on November 27 1978 for program in the Salt Lake Tabernacle
One ex-Mormon on the Recovery from Mormonism message board claimed to have located an "the actual photograph" of the 11 March 1977 meeting on LDS.org!  That photograph, however, is actually of a meeting in the Tabernacle on November 27, 1978.
This meeting was documented in the January 1979 Ensign:
Two presidents saluted the family as one of life’s greatest institutions at a special November 27 program in the Salt Lake Tabernacle, culminating National Family Week in the United States.
Before a capacity crowd, with national and international television cameras whirring, President Spencer W. Kimball urged his listeners to recognize the family as “our chief source of physical, emotional, and moral strength.” He presented United States President Jimmy Carter with a bronze statuette depicting the family circle. The miniature of a father, mother, and child is based on the original work by Utah sculptor Dennis Smith, Circle of Love, one of the pieces in the Relief Society monument to women in Nauvoo. 
President Kimball wrote a letter to President Carter in May 1977 to present a copy of Carter's genealogy
President Kimball wrote a letter to President Carter in May 1977, only two months after the March 11 meeting:
W. Don Ladd, Regional Representative of the Twelve, and Thomas E. Daniels of the Genealogical Department of the Church presented a family tree and a leather-bound volume of genealogical information on the Carter family to the President on 31 May.
The book included a letter to President Carter from President Spencer W. Kimball, in which he spoke of the Latter-day Saints’ “deep reverence and gratitude for our ancestors, which in turn gives us greater sense of responsibility to our posterity.”
President Carter found the Church’s research “very exciting to me,” and he said, “I look forward to studying the chart. This is an area of knowledge I’ve never had.” The two-inch thick volume included several 8-by-10-inch pedigree charts and family group sheets, along with a research summary of each line researched and what was still missing from those lines. This is the first time the Church has ever given such a gift to a president of the United States. 
The allegation that the LDS church's tax-free status was threatened in 1978 seems to have originated in 2001
A claim that the federal government had threatened to revoke the Church's tax-exempt status back in 1978 was made by a woman named Kathy Erickson in a letter to the Salt Lake Tribune on March 11, 2001. Erickson stated,
Gainful Revelation Date: March 11, 2001
What’s done is done. There no longer is any prejudice against blacks in the Mormon church, the power of money took care of that. Back in 1978 the federal government informed the LDS Church that unless it allowed blacks full membership (including the priesthood) they would have to cease calling themselves a non-profit organization and start paying income taxes. On $16.5 million a day in tithing alone that’s a lot of tax monies that could be better used in building up the Kingdom of God.
The church immediately saw the error of its ways and the brethren appealed to God for a revelation; it came quickly. God works in mysterious ways, His wonders to perform, and today The Church of Jesus Christ of Latter-day Saints has nothing but love for all races of people on Earth.”
A representative of the Church Public Affairs department responded:
Distorted History Thursday, April 5, 2001
It's one thing to distort history, quite another to invent it. Kathy Erickson (Forum, March 11) claims that the federal government threatened The Church of Jesus Christ of Latter-day Saints with its tax-exempt status in 1978 because of the church's position regarding blacks and the priesthood.
We state categorically that the federal government made no such threat in 1978 or at any other time. The decision to extend the blessings of the priesthood to all worthy males had nothing to do with federal tax policy or any other secular law. In the absence of proof, we conclude that Ms. Erickson is seriously mistaken.
BRUCE L. OLSEN Public Affairs Department The Church of Jesus Christ of Latter-day Saints 
'Tópicos do Evangelho: "as autoridades da Igreja encontraram negros fieis e antepassados mórmons de origem diversa que haviam contribuído financeiramente e de outras maneiras para a construção do Templo de São Paulo, um santuário que perceberam que não lhes fosse permitido entrar uma vez concluído"
"As Etnias e o Sacerdóciod," Tópicos do Evangelho (2013):
O Brasil, em particular, apresentou muitos desafios. Ao contrário dos Estados Unidos e África do Sul, onde o racismo legal e de fato levou a sociedades profundamente segregadas, o Brasil se orgulhava em sua herança racial aberta, integrada e mista. Em 1975, a Igreja anunciou que um templo seria construído em São Paulo, Brasil. Como a construção de templos prosseguia, as autoridades da Igreja encontraram negros fieis e antepassados mórmons de origem diversa que haviam contribuído financeiramente e de outras maneiras para a construção do Templo de São Paulo, um santuário que perceberam que não lhes fosse permitido entrar uma vez concluído. Seus sacrifícios, bem como a conversão de milhares de nigerianos e ganeses na década de 1960 e início dos anos 70, tocou os líderes da Igreja.—(Clique aqui para continuar)
- Jan Shipps, "The Mormons: Looking Forward and Outward" Christian Century (Aug. 16-23, 1978), 761–766 off-site
- The Daily Diary of President Jimmy Carter, Jimmy Carter Library & Museum off-site
- "According to the President Carter Library,” posted by "CLee the Anti-Mormon," 8 February 2006.
- "Church Honors President Carter’s Support of the Family," Ensign (January 1979)
- "Church Give Genealogy to President Jimmy Carter," Ensign (August 1977).
- Kathy Erickson, letter to the Salt Lake Tribune, 11 March 11, 2001.
- Bruce L. Olsen, cited in Salt Lake Tribune on 5 April 2001.
- "As Etnias e o Sacerdócio," Tópicos do Evangelho (2013)