George Weigel attempts to capture its essence and effect:
[T]here is the mythology surrounding Kennedy’s 1960 speech on church-and-state, delivered to the Greater Houston Ministerial Association. No one should doubt that hoary Protestant bigotry was an obstacle the Kennedy campaign had to overcome in 1960. Still, a close reading of the Houston speech suggests that Kennedy neutralized that bigotry, not only by deft rhetorical moves that put bigots on the defensive, but by dramatically privatizing religious conviction and marginalizing its role in orienting a public official’s moral compass. Thus Kennedy became, in effect, a precursor of what Richard John Neuhaus later called the “naked public square”: an American public space in which not merely clerical authoritarianism, but religiously-informed moral conviction, is deemed out-of-bounds.
Finally, there is the phenomenon that might be called the Kennedy Catholic: a public official who wears his or her Catholicism as a kind of ethnic marker, an inherited trait, but whose thinking about public policy is rarely if ever shaped by Catholic social doctrine or settled Catholic moral conviction. The many Kennedy Catholics in our public life are one of the last expressions of urban (or suburban), ethnic, Counter-Reformation Catholicism in America; and as such, they evoke a certain nostalgia. Unfortunately, the shallowness of their Catholic formation and the invisibility of Catholic moral understandings in a lot of their judgments make Kennedy Catholics de facto opponents of the Church’s mission in the postmodern world, not protagonists of the culture-reforming Catholicism of the New Evangelization.