Why are they expected to be different on different planetary bodies without sharing of materials? Is the early solar nebula kind of like a reverse centrifuge with denser isotopes near the sun and lighter ones further away?
It's not that they're expected to differ, it's that they do differ. If you look at oxygen isotopes from meteorites the ratios are all over the place. Also, Mars meteorites (which we know are from Mars because of noble gas isotope ratios being the same as measured by Viking landers) have different oxygen isotope ratios than Earth.
All rocks on Earth and on the Moon have ratios that lie on a single line, the Standard Mean Ocean Water (SMOW) line.
BTW, the fact that meteorites have a wide variety of ratios that don't lie on a single line indicates meteorites derived from asteroids did not come from a single parent body. There was no planet between Mars and Jupiter that exploded to form the asteroid belt, bad science fiction stories notwithstanding.
