biochemistry - Hydrophilicity and polarity

I think the answer is no.

The definition of polarity is basically that a molecule has a dipole, and as water has a very large dipole, if a molecule will mix with water readily, its usually pretty polar.

Water also can share its hydrogens in hydrogen bonding, which is an actual shared covalent bond where a hydrogen atom is shared between two acceptors. The hydrogen bond is fairly weak (~ 0.5 kcal/mol) but water does a lot of hydrogen bonding.

So hydrogen bonding and polarity are often a shared characteristic of an molecule, but are not the same thing.

Ions are quite hydrophilic but do not need to be hydrogen bond donors or acceptors. Chloride (Cl - ) is not a hydrogen bonding atom - its so acidic that it exists nearly entirely in the Cl- form in water solution. But its definitely electro negative and really soluable in water. Are Ions polar though? Chloride is symmetrical and so its not really polar.

Still is there a polar molecule which is neither a hydrogen bond donor or acceptor? Acetone and the cyanide ion (CN-) are a polar molecules which have no hydrogen bond donor, but can accept them.

I think sulfate is an example of a polar molecule which does not form hydrogen bonds.
Sulfate (SO4 -- ) has four S-O bonds arranged in a tetrahedron but each of them is highly polar - with 90% of the negative charge on the oxygen. But like the Chloride ion its so acidic that it much prefers its free ionic state. It would have very little hydrogen bonding character even when its in water. Sulfate can form hydrogen bonds, but I think they will only be stable when there are several of them at once. Sulfate binding protein has seven hydrogen bonds when it binds sulfate, using the chelation effect to make the binding strong enough to be stable.