If a State allowed nude dancing, a ruling by USSC stating it is not protected by the First Amendment would not [allow a nude dancing law to] be overturned by litigation. It could be overturned by legislation.
Eventually. In the above scenario, I would imagine that a suit would be filed claiming that nude dancing violates the state's obscenity law. Since it has no more 1st amendment protection, the activity would be found in violation of state law (on obscenity). There would be a court order for that activity to stop.
Based on that local ruling (and assuming no appeals), I would imagine that the legislators would then change the law.
Or the petitioners could go to the legislature first to change the law. Then the nude dancers would file suit with the same result. Probably a waste of time.