That is my understanding of what Catholicism teaches. No one who understands what Catholicism teaches should have an issue with that. You don’t. I don’t. That leaves asoul.
Why are they considered Catholics if they don’t believe what Catholics are required to believe?
Great question.
There could be different answers....I've never spoken about this to any priest in any great length..
I'll tell you what one said to me ... a traditional priest, about 10 years or more ago.
I asked him....what if someone doesn't believe a dogma?
He said to pray about it.
What else could they say? "You're anathemized"?!
Should they be ex-communicated?
The Catechism of the Catholic Church states that obstinate denial is a sin.
So,,, we don't make it be obstinate! We pray about it.
Plus,,,different priests believe differently in the sense of being more conservative or less conservative.
Other than that,,,,I have no other idea.
CCC 2088 The first commandment requires us to nourish and protect our faith with prudence and vigilance, and to reject everything that is opposed to it. There are various ways of sinning against faith:
Voluntary doubt about the faith disregards or refuses to hold as true what God has revealed and the Church proposes for belief. Involuntary doubt refers to hesitation in believing, difficulty in overcoming objections connected with the faith, or also anxiety aroused by its obscurity. If deliberately cultivated doubt can lead to spiritual blindness.
CCC 2089 Incredulity is the neglect of revealed truth or the willful refusal to assent to it. “Heresy is the obstinate post-baptismal denial of some truth which must be believed with divine and catholic faith, or it is likewise an obstinate doubt concerning the same; apostasy is the total repudiation of the Christian faith; schism is the refusal of submission to the Roman Pontiff or of communion with the members of the Church subject to him.”1