Now, another Massachusetts politician with an eye on the White House -- Republican Gov. Mitt Romney, a Mormon -- faces a similar problem as he confronts suspicions among his party's base that his church is at best a non-Christian sect and, at worst, a cult.
A recent Bloomberg/Los Angeles Times poll shows what Romney may be up against. A full 37 percent of Americans said they would not vote for a Mormon candidate; only Muslim candidates, at 53 percent, had higher negative ratings.
In order to mute questions about Mormon theology and practice, Romney, like Kennedy, will have to declare his independence from his church -- but with a twist: Where voters once needed to know that a candidate's faith would remain private, many voters today, especially Christian conservatives, need to be assured that a candidate's faith will guide his decisions -- even if, as in Romney's case, they don't agree with its doctrine.
"It can't be a repeat," said Charles Haynes, a First Amendment scholar at the Freedom Forum in Arlington, Va., and an expert on American religious and political history. "His Kennedy moment has to be much more nuanced. He has to speak the language of faith without being too particular" because of the differences between his faith and traditional Christianity.
"And he has to assure the rest of the country that he can reach across these religious divisions and party lines and be president of all the people."
The Rev. Richard John Neuhaus, editor of First Things, a magazine of orthodox Christian thought and opinion, also thinks Romney will have to make a Kennedyesque speech. But, he cautions, there are risks. "He runs the very great risk of alienating his Mormon supporters if he distances himself too far from the (Mormon) Church," he said. "And it could also alienate a lot of evangelicals who may see it as a waffling about religious convictions."
Mormons and traditional Christians do have their differences. Both take the Bible as Scripture, but Mormons have additional sacred texts, including "The Book of Mormon," which they believe was divinely revealed to their prophet, Joseph Smith, in 1830.
Mormons believe theirs is "the one true church," something that riles more traditional Christians. Mormons also believe God had a physical body and literally fathered all human souls and have their own view of the Trinity. Both groups believe salvation comes through Christ, but Mormons do not believe in original sin. Currently, mainline Protestants and Catholics do not recognize Mormon baptism.
"Do Mormons have differences with evangelicals? Sure we do," said Scott Gordon, president of the Foundation for Apologetic Information and Research (FAIR), an organization that defends Mormon theology. "Otherwise there would not be a Mormon church."
"He's got to say his faith will have an impact, but his denominational beliefs will not. If he can do that, he can win over evangelicals because they would have a person of faith in the White House who would not be following what they would see as the whims of the Mormon church."
The Church of Jesus Christ of Latter-day Saints, which claims 5.5 million members nationwide, endorses no parties or candidates. "The church is politically neutral," said Michael Otterson, a spokesman for the church.
"We ask LDS candidates not to imply in any way that they are endorsed by the church." The church also makes no campaign donations to anyone.
Romney graduated from Brigham Young University and did a missionary stint in France. Prior to his election as governor, the father of five and grandfather of nine served as a regional stake president overseeing Mormon congregations and led his church as a bishop.
Robert Millet is a professor of ancient scriptures at Brigham Young University and a veteran of Mormon-evangelical dialogue. He says Romney must address his religious beliefs before someone else tries to exploit the Mormons' history with polygamy (outlawed in 1890) and racism (African-Americans were denied full membership until 1978).
"He will have to make the point that if you want to understand me, look at 21st century Mormonism and not at its anomalies," Millet said. "He will have to say if you want to know what I believe, ask me, don't tell me."
Romney may not be willing to do that. His office declined requests for an interview, and in a June interview on "The Charlie Rose Show," Romney deflected specific questions about his religion.
"(I)f you have doctrines you want to talk about, go talk to the church,"
he told interviewer Judy Woodruff when she asked about specific Mormon beliefs. "Because that's not my job."
Romney is not the first Mormon to face opposition to his faith in pursuit of the presidency. His father, Michigan Gov. George Romney, ran for the Republican nomination in 1968, losing to Barry Goldwater. Conventional wisdom at the time was that his faith was more hindrance than help.