FairMormon 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.
Question: Was the priesthood ban lifted as the result of social or government pressure?
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." 
- Jan Shipps, "The Mormons: Looking Forward and Outward" Christian Century (Aug. 16-23, 1978), 761–766 off-site