Look closely enough and you'll see that they all do. One meaning for 'heterodox' is 'holding unorthodox opinions'. That's an attribute of the person, not the opinion.
The royal road to clarifying subtle differences in language, however, is etymology, and there the difference is plain. Hetero = different, dox = opinion, ortho = correct. So the distinction here is something like "diverse opinion" vs. "incorrect opinion", which to me seems clearly meaningful.
> The royal road to clarifying subtle differences in language, however, is etymology
No, it's not. Etymology tells you where a word came from, not what it means (either in denotation or connotation) in current usage. It will often be completely misleading in trying to unpack subtle differences in meaning.
The royal road to clarifying subtle differences in language, however, is etymology, and there the difference is plain. Hetero = different, dox = opinion, ortho = correct. So the distinction here is something like "diverse opinion" vs. "incorrect opinion", which to me seems clearly meaningful.