Now we get to the essence of the argument. The Gospels, particularly St. John, tell us that those who believe in Him will have eternal life. Assuming for argument sake that Bishop Budde believes in Jesus (albeit it with great error with respect to Catholic teaching) because her reason assures her she is right is she saved? If not, is it a matter of the degree of belief or a matter of the degree of error?
Peace be with you
Without knowing a person's full belief on the doctrine, I don't think it is productive to argue hypotheticals. The article stated this bishop conjectured about, rather than denied the resurrection:
"Believing on Jesus Christ" obviously means more than believing he existed. Neither you nor I can judge another's salvation since we cannot see their heart. Whether salvation depends on the "degree" of error or truth, I would say Scripture makes it quite clear that we are saved by the grace of God THROUGH faith and that not of ourselves. Can people be in error about certain aspects of the faith and still be saved? To a degree, yes, since those who were saved by faith in Christ had to learn about all that the faith entailed. The advantage new believers have is the indwelling Holy Spirit, who will lead us to the truth. No one who has the Spirit of God will deny Christ is God, that he arose from the dead or that he forever lives to make intercession for us. Thank God he doesn't insist on a spotless memorization and recitation of the Catechism before making us His own!
I bid you peace, as well.