The terms attempt to classify people based on an arbitrary collection of visually distinct phenotypes rather than fundamental genotypes -- however, the One-drop Rule (https://en.wikipedia.org/wiki/One-drop_rule) works only on the basis of the latter. This inconsistency alone makes the terms scientifically irreconcilable.

Well, that straw man is obviously useless, which is why the bad old days had an intense vocabulary for all the different proportions of mixed race. Research today shows that people's classifications generally lines up with genetic ancestry. So, for example, doctors are well served to judge racial/genetic makeup by appearance when diagnosing and treating patients. Likewise, if you want to make an ethnostate or the opposite, it's certainly a useful concept. (American immigration laws by design do the opposite, using national quotas as a proxy for race.)