>>> import pandas as pd >>> pd.CategoricalIndex(['a', 'b'], categories=['a', 'b']).equals( ... pd.CategoricalIndex(['a', 'b'], categories=['b', 'a'])) False

I fixed this for regular Categoricals in #16339, but that didn't affect CategoricalIndex.equals. Do we want .equals to ignore order when ordered=False on both (I think we do)?

Discovered during my CategoricalDtype refactor, which does fix it so that order is ignored when order=False.