Not sure how the Supreme Court could resolve this on standing. Article III is not a barrier to standing in state court and the Constitution, of course, still applies there.
Unsure how any "Republican voter" is harmed by the decision of the RNC to run any candidate. Bascially there is a reason they had "Republican voters" file this suit.
But yes this would be two part
1. State Courts can't do this at all
2. Only the Attorney General(or a specific set off officials) can bring enforcement action - otherwise the proper forum is the same for ruling individuals ineligible for Congress. Congress
The Supreme Court cannot allow this to ever happen again. I am almost certain their number one priority will be killing Section III, not anything to do with Donald Trump. What is going on right now is an existential threat to the court system and it is obvious from the behavior of the 5th Circuit and everyone's favorite Texas district judge that the claims "its self evident this only applies to 1961 AND Jan 6th, 2021" will not stop the court from having to kill it later if not now.
Seriously, if Trump's disqualification stands what about any senior officials who took part in efforts to overturn the election? What about Senators who voted for the challenges? Mike Lee who was in discussions?
Is the Speaker of the House, third in line for the Presidency, ineligible?
There is no way to restrict this to Donald Trump and therefore any ruling pretty much has to ensure no court will try to disqualify anyone under Section III going forward for Jan 6th.
There's a pretty easy way for the court to handle this sort of thing without gutting Section III completely.
Congress has already defined "insurrection" under 18 USC § 2383. One of the penalties even outlined in this statute is disqualification from office.
So the court can simply rule that if someone is convicted under 18 USC § 2383, they are disqualified for public office. If they are not, then it doesn't apply. Pretty simple and binary.