You have a very flexible definition of "unchanged" then. The Catholic Church pre-Charlemagne is going to be very different from Saeculum Obscurum-era, itself different from Investiture Crisis-era, itself different from the one familiar in the Late Medieval, different from Counter Reformation-era one. It's absurd to me that you think the first time it changes significantly is Vatican II!
> Ancient Egypt was already thousands of years old when Socrates harassed aristocrats in Athens.
My knowledge of Ancient Egyptian history is extremely poor, but what little I do know strongly suggests that considering it as a single stable form of government for thousands of years is even worse an error than claiming the Catholic Church was so stable and unchanging. Perhaps akin to saying that the Holy Roman Empire, the German Empire, the Weimar Republic, the Third Reich, and modern Germany are all one single country that has lasted for 1200 years (because they're all called Germany).