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.
That's the whole point. The full faith and credit clause doesn't invalidate state laws, it requires that states recognize the public acts and judgments of other states. That's why a Nevada marriage is recognized in the other 49 states.
"S. Ct." stands for the Supreme Court reporter.