I've been reading through the many posts about whether Muslims worship the same God as Christians, and it got me wondering about the more general question (maybe answered in the thread, but I don't have the time to read through 100+ posts, and it may be worth repeating in a shorter thread).
How far does it go? If I accept God, but think He did different things, for example established an invisible and not visible church, thinks the Eucharist is symbolic, was an iconoclast... basically, if God is a Southern Baptist, is that God still the same? What is the breaking point? What are the essential parts of God when, if I believe something different, I'm no longer thinking of God but of some other god or being?
It seems like there are various levels of disagreement:
When is it acceptable for a Catholic to just have different ideas about the faith? When is that a point in which the Catholic is breaking off from the Church? At what point does it become material heresy? And at what point do you start a new religion?
Finally, what point does your new religion begin to worship a new god, and not the same god as the Catholics worship?