IIRC, the parties own the primary process; it has nothing to do with the Constitution. That being the case, the Dems can decide to only run primaries in CA, NY, OH, FL, and PA if they want. If they don't run a primary in your state, presumably you can vote in some other parties primary...However, they did make a rule, which Michigan and Florida violated, and the party punished those states - all of the candidates at the time agreed to this outcome.
As Will rogers once said - "I don't belong to an organized political party...I'm a Democrat"