Is this term relevant??? Molecular oxygen, as a gas, has low solubility in water. hydrophobic - hydrophilic - who cares?
Balancing dipole interactions give it no net dipole. Thus you cannot say it is polar - despite that carbonyl's, hydroxys, etc are all polar.
I think what you really mean is, can it cross a PM. Yes, barely, and better than charged ions/huge macromolecules. But it does not do it that well.
Remember, Oxygen needs hemoglutan to be transported in the blood
IF IT WAS HYDROPHOBIC, it would aggregate with lipids. I do not think it does this. It is NEITHER>