For much of American history, the pope was anything but irrelevant. Throughout the 19th century, Protestants feared him, concerned he and his minions were plotting to take over the United States from afar and replace our Constitution with their canon law.

As late as the 1960 presidential election, John F. Kennedy felt it necessary to promise (in his now famous Houston speech) that if elected president, he wouldn’t be taking orders from the Great and Powerful Vatican.

Today the gap between the “official” Catholicism of Rome and the “unofficial” Catholicism of communicants in Cincinnati and Des Moines is wide and growing.

If you ever find yourself offering an introductory lecture on Roman Catholicism you might find yourself saying things like “Catholics believe the pope can speak infallibly” or “Catholics require their priests to be unmarried men” or “Catholics reject artificial birth control.”

Yet in a New York Times/CBS News poll released this week, nearly four out of every five U.S. Catholic respondents say they favor artificial methods of birth control. Nearly two-thirds say they favor letting Catholic priests marry, and another two-thirds say they favor women’s ordination. Moreover, American Catholics today are more likely to say the pope is “not infallible” (46%) than they are to say that he is (40%).

And so it goes in this survey on questions such as abortion, the death penalty and same-sex marriage, where a majority of rank-and-file U.S. Catholics disagree with the Catholic hierarchy.