1-hexanol is polar
Hardly, it has a huge, nonpolar, aliphatic group, -OH is just a small part of the molecule.
while oxalic acid is apolar (being symmetric, its dipole moment dipole is = 0)
Polarity is not just a function of a dipole moment, it also depends on the whole molecule shape and properties of its parts. Oxalic acid has two carboxylic groups, both quite polar. Just because their dipole moments cancel out doesn't mean they don't interact strongly with water.
Plus, polarity is mostly a relative concept - it helps us compare molecules, which one is more polar than the other, but it is not a well defined, quantitative concept.
"Similar dissolves similar" is just a rule of thumb, no wonder it fails. But once you get the polarity concept right it is quite OK, we have no better, general ones that could be used as easily.