How far left?

So, here is my question, how far away does someone have to be from Church teachings and/or doctrine, that they cease to be Catholic, even if they call themselves Catholic?
I am not talking about politicians who are pro-abortion and continue to go to Mass and receive communion. I am talking about dissent so strong it stops looking Catholic at all. For example, women who have been ordained by a bishop in the "Old Catholic Church," sisters who think that homosexual relationships should be blessed by the Church, and that it would be better if males and females were androgynous. How can these people call themselves Catholic? All of these examples come from a book I just read called, "Good Catholic Girls" by Angela Bonavoglia. I read the book to learn what "liberal" women are interested in changing about our Church. Angela is a Catholic journalist and interviewed various women on the forefront of trying to change our Church. Much, if not all, was a sad commentary on how misguided people can become when they rely on their own wisdom and power. The only chapter worth thinking about is the one on the sexual abuse problems in the Church.
Each of the women still call themselves Catholic, though I am hard pressed to see why. The only belief none of them disputed, was the Real Presence. All the other teachings and doctrines were in some way corrupted to fit their own version of Catholicism.
So, because they beleve they are Catholic, are they?