When the commutator of two operators vanishes then we can measure one without affecting the other. I'm not sure how this translates in the case of density matrices.
If the density matrices are representing pure states then the density matrices would represent projection operators onto the subspace spanned by the given state. So I think a vanishing commutator on two density matrices could mean that either the subspace spanned by the two states are orthogonal or that they are the same. Is this correct?