I don't believe that is correct. The due process rights being violated must be those of a citizen of that state. So, it is possible that a state law could be so arbitrary that it denies a citizen due process, or otherwise infringes on that citizens constitutional right. In that case, the US Supreme Court could take the case even though the underlying matter is purely one of state law.
But in this particular instance, there is nobody's due process right being violated by a state judge saying abortion is legal. And you can't argue that its the right of The unborn fetus because the US Supreme Court already said that is not a federal right that can be protected.
What about the people of MN and their state legislators?
The people of MN elected their state legislators. Their state legislators man anti abortion laws.
If the MN ruling arbitrarily strikes down these laws (I've not read the MN Constitution, nor the laws), then the due process rights of the people of MN are being abridged.