Anti-Catholic bigotry helped to keep Catholics from many political offices well into the 20th Century; it was not until 1928 that a major political party, the Democrats, were willing to risk nominating a Catholic, and that man, Al Smith lost largely due to a coalition of factors but Anti-Catholic sentiments played big part in Smith's defeat.
The argument, against Smith, other Catholics, and eventually Kennedy, was that their loyalty would be to The POPE in the Vatican, first, America second. Catholic Kennedy faced this argument head on, unflinchingly declaring that he was a loyal American. What truly put Kennedy over the top, as regarding his nomination, was winning a primary in West Virginia a state that to this day in 2009 proudly loudly 'hates' Catholics. Once West Virginia said "Yes" to Kennedy, his nomination was assured, and when the dust settled, in the climate of 1960. the Catholic issue was anti climatic.
Odd note - - - Catholics can shoot themselves in the foot. Catholic John Kerry in 2004 was largely defeated because though a Catholic, he was divorced and had remarried without permission from the Church, and John Kerry as a Liberal was 'suspected' of supporting 'gays' as well as pro-choice, but the true kicker was that as a soldier during Vietnam, Kerry killed people. Catholic Bishops and Priests denounced Kerry as a murderer, a pro 'f%ggot Liberal Baby Killer, a Divorce Sinner, and worked overtime to reelect Geo Bush who admittedly never killed anyone though he did launch two wars which have to date killed more than a hundred thousand people. Catholics can be a hoot.