What does it mean to be a Catholic? I

I would like to probe a little further Father Araujo’s statement that “I am mindful that there are those who consider themselves members of the Catholic Church but still challenge Peter while at the same time proclaiming their individual fidelity to the Church. . . . Whether anyone elects to bear allegiance to Peter is up to himself or herself. Should this person decide to depart from this loyalty, he or she leaves the Church notwithstanding personal protestations to the contrary.” Although there are distinctions, the statement reminds me of the November 14, 2006 statement of the U.S. Conference on Catholic Bishops, http://www.usccb.org/dpp/Eucharist.pdf, in which it condemned “selective assent to the teachings of the Church” and stated that those who “knowingly and obstinately repudiate her definitive teachings on moral issues” should not receive communion.

Between 1963 and 1974, for example, the majority position of American Catholics shifted away from that of the Vatican on issues such as whether sex before marriage was always wrong (from 74% to 35%), whether divorce after marriage is always wrong (from 52% to 17%), and whether contraception is always wrong (from 56% to 16%). Andrew Greeley,The Catholic Revolution: New Wine, Old Wineskins, and the Second  Vatican Council 39 (Berkeley, California: University of California Press, 2004).

   Indeed, American priests, according to Greeley, also engaged in selective assent to the teachings of the Vatican. The Vatican, for example, maintains that homosexual relations, masturbation, and artificial birth control are always wrong, but only 56% of priests agreed with the Vatican’s teachings on homosexuality, 28% on masturbation, and 25% on birth control. According to the Bishops, should these Catholics not receive the Eucharist? Should these priests not be saying mass? Are they not obstinate? Are the teachings not definitive? Does departure on any single moral issue separate one from the Church or does it depend on the nature of the issue(s).
    For example, Richard McCormick argued that little deference to the  Vatican should be paid on issues relating to sexuality and women for a variety of what struck me as good reasons. Should he and those who thought like him not participate in the Eucharist?

These are obviously important issues and I wonder whether the generality of the Conference of Catholic Bishops general statement was designed to steer clear of them.  Clearly , at some point, rejection of Vatican teachings separates one from the Church. Have most American Catholics already done so according to Father Araujo? The Conference of Catholic Bishops? Other  MOJ participants?