Your question is based on a chain of implications, most of them containing some quite common misunderstanding in statistical thermodynamics.
For a truly homogeneous mixture, there is uniform distribution of the solute in the solvent. But, only if the solute particles are equidistantly distributed, there will be perfect homogeneity.
True. In a homogeneous mixture, there is uniform distribution of the solute in the solvent. More formally, if we introduce the number density of the solute, $\rho_{solute}({\bf r})$, we have:
$$
\rho_{solute}({\bf r})=\mathrm {constant}.
$$
However, $\rho_{solute}({\bf r})$ is an average quantity, therefore its constant value implies that in every small volume element there will be in average the same number of solute particles. In turn, this implies the existence of an average inter-particle distance. It does not imply that particles are always equidistantly distributed.
That is, if there is no equidistant distribution, there will be certain "regions" where there is more solute concentration than the rest of the solution, hence no homogeneity. But if there is equidistant distribution of the solute to attain homogeneous, the system will be in a highly ordered state,
As noted above, since homogeneity is equivalent to a constant average density, in a scale of ordering where the crystalline solid is the most ordered structure, corresponding to a non-constant $\rho_{solute}({\bf r})$ having the same spatial periodicity of the crystalline lattice, $\rho_{solute}({\bf r})=\mathrm {constant}$ represents the maximum spatial disorder.
It may appear that some arbitrariness or subjective judgement is connected with this scale of ordering. It is true, and this is pointing to the inconsistency of using spatial disorder as a proxy of entropy, but for very special cases like weakly interacting systems.
implying the system has minimum entropy.
In any case, this last implication (maximum spatial order $\Rightarrow$ minimum entropy) is not always true. Otherwise, it would be impossible to have stable phase separated mixtures. Mixing seed oil and water in a glass allows everybody to check that phase separation may be the stable configuration as well as global homogeneity for other systems. What makes the difference is the presence of different inter-particle interactions.
When connecting entropy with disorder, one should bear in mind that the only general connection between these two concepts, justified by statistical mechanics, is that disorder should be measured by the spread of probability of the set of states. It coincides with a uniform one-particle density only if interactions are small enough.
