As punishment for moving up primary, DNC strips Michigan of convention delegates

BTW, how is the RNC reacting to this primary-scheduling fracas? The state legislation in question applies to both parties, after all.

What are the legal implications of this? IANAL and political parties are private organizations - BUT primaries are run (and paid for) by the state and thus should have SOME legal standing.
Could a XIVth Amendment argument be made that not seating the delegates violates the Constitution? What would happen if in the pissing contest, a state were to take away the party-based primaries or punished a national committee by not recognizing the party?

They do. They have the right to run the primary, no more and no less. If the state were to go for a third party candidate, could the parties sue because the state has no delegates to send to their conventions? I think not.

The state can refuse to participate, whatever benefit that would get them. If the parties fulfill the requirements for getting a candidate on the ballot the states have to let them participate in the primary, unless they opt not to have one.

They could also have an open primary with no party distinction, much like a general election, but then they would only be able to influence one national candidate.

I don’t think so. How a political party selects its candidates is none of the state’s business.

But it is a state’s business to decide who qualifies to run as a candidate in their state.