Whether by accident, serendipity or divine design, four future heavyweights of American Catholicism found themselves in the Class of 1962 at St. John’s Seminary.

Momentous societal changes were surfacing all around the young men, but seminary life for George Niederauer, Roger Mahony, William Levada and Tod Brown continued much the same as it had for centuries. The four friends — a pair of cardinals-to-be, a future archbishop and bishop — were assigned alphabetically to desks and dorms. They arose at 5:30 a.m. and, within a half hour headed to the chapel for prayers and Mass. Silence was required during meals and after 7:30 p.m. Moral theology and philosophy classes were taught in Latin.

The priests-in-waiting had neither televisions nor telephones and were forbidden to leave the campus in Camarillo, Calif., without permission. They could read about current events — such as the 1960 election of the first Catholic to the White House — but only in clips from approved newspapers....