Someone asked recently so I thought it good to make something clear: in my homily this last Sunday I mentioned the necessity for Catholics to accept all that the Church teaches. This is, after all, what it means to be Catholic: to believe "One, Holy, Catholic and Apostolic Church". To clarify, however, this does not mean that Catholics are required to believe everything that claims to be Catholic. There are many out there who make claims about the Catholic faith that are completely inaccurate. I once heard someone tell me that he was certain that the Catholic Church believed that Mary had become the fourth person of the Trinity (!).
In believing all that the Catholic Church teaches, I am referring to the dogmatic statements that the Church has declared; this is the "ex cathedra" level of authority. The Church's dogmas are those things held to since the first century, and only those truths that are in accord with them. You are not required (and, technically, are forbidden!) to accept anything that is not in accord with the fullness of the Catholic faith as always believed since the first century.
Even a Pope could say something contrary to the faith (we pray it does not happen, but it has before and it can happen today). To believe otherwise is not the Catholic faith (though it is often claimed to be so by Protestants). There is a difference (though there should not be) between the words of a clergyman and what the Church actually teaches authoritatively. Please be clear about that. To believe what the Church has always taught and reject things that are not in accord with that truth is not unfaithful, but faithful.