So now the Supreme Court of the United States is not a federal court. OK. I'm enjoying this visit to the Twilight Zone.
In the Twilight Zone no state has any obligation to recognize marriages recognized by other states. Whenever a couple moves across a state line they have to get remarried.
Those index citations you provided weren't the usual for the USSC. Since the posting of your comment, I did find the rulings, and for Sutton vs. Leib, the more standard index citation is 342 US 402. I don't know what "72 S.Ct. 398" was supposed to refer to, but that's what threw me off.
In any case, I did look over the ruling on Findlaw, and I answered my own question as to whether this nullified any aspect of Illinois law. It did not. This simply was not a case that involved a conflict between the laws of two different states, so therefore it's irrelevant to this discussion.
Whenever a couple moves across a state line they have to get remarried.
Complete distortion of my position, and I think you know it.