A 1999 survey by National Catholic Reporter on American Catholic Beliefs (note, some of the beliefs are required dogma).
"The purpose of inquiring into Catholic identity is to describe more precisely this aspect of the actual lived faith of Catholics, which may or may not fit exactly with official teachings. All religious groups have elements of popular religion that develop among the faithful. The Second Vatican Council reaffirmed that the sensus fidelium -- the sense of the faithful -- is important.
Anyone investigating Catholic identity soon finds that being a Catholic has many possible facets. The Catholic tradition is old, rich, variegated, and for some, bewildering. There are saints, social reformers, relics, mystics, spiritual virtuosi, devotions, obligations, art forms, institutional rules and hundreds of moral teachings. What are the most central and the most important facets? What most defines what being a Catholic really means?"
"The table also shows attitudes broken down in three levels of education. Catholics with different levels of education differ on only two of the six ratings. On the fourth, concerning Mary, the Mother of God, the most educated Catholics have a lower rating than the others; the difference between the most and least educated groups is 16 percentage points. And on the sixth, concerning the teaching authority claimed by the Vatican, the most educated Catholics have a much lower rating than the others...[only 28% of those with a college degree said "the teaching authority claimed by the Vatican" is very important to them.]
Here is an indication of trends in the future. Since educational levels among American Catholics are steadily increasing, we may expect future Catholics to resemble the more educated Catholics today. Probably future Catholics will attach less importance to devotion to Mary and to church authority."
(23% of Catholics polled believe a person could be a good Catholic and not believe in the bodily resurrection of Christ. 38% of Catholics polled believe a person could be a good Catholic and not believe in the real presence of Christ in the eucharist. 77% of Catholics polled believe a person could be a good Catholic and not go to Mass every Sunday. 72% of Catholics polled believe a person could be a good Catholic “without obeying the church hierarchy’s teaching on birth control".)