Setting aside the comments about Episcopalians in particular (which I can understand an Episcopalian being offended by), the heart of your question seems to be why Catholics who don’t accept every teaching still stay Catholic.
This question comes up on the forums periodically and I always post a link to this article when it does:
Why I’m Still Catholic by Fr. Greely
Really, there are many different kinds of “cafeteria Catholics”. Some are lukewarm and don’t pay close enough attention to Catholic things to ever experience any sort of mental disconnect between the Profession of Faith and what they actually believe. But others are very well informed – probably more so than the majority of us CAF posters – and even work in various positions within the Catholic Church. The answer to the question “Why don’t you just leave?” is going to be different for them.
For those who are more involved, yet still question certain teachings, I think they would counter with the question: Do you leave your family just because you disagree with some of them? And the answer is: Of course not. So why leave the Catholic family? Why leave the faith that is their home?
You and I may realize that certain teachings are not going to change. But they would not see it that way. And they would see their continued presence as a witness to the change they believe needs to take place. Reform comes from within, not from without.
I think we need to be very careful about these types of conversations as the potential to offend and foster a spirit of animosity is very high. We should not be about kicking the “unfaithful” to the curb (or sending them somewhere else to be someone else’s problem). We should be about conversion of hearts and minds.