As I guessed at the start, Im sticking with 7-2 against unfettered nationwide injunctions. Its really clear as mud on how this well specifically go, but here's my guess:
Sotomayor and Brown will stick with saying Article III gives courts wide power to fashion any remedy.
Thomas will say article III no inherent power for judges to order injunctions for non-parties. Congress needs to create that power. Alito didn't really signal anything other than "what's the point of this?" But based on history, he likely aligns with Thomas.
So that leaves 5 justices to say under what circumstances the nationwide injunctions are allowed.
Kavanaugh is in the "class action" camp. And would include injunctions for a putative class before a class is certified.
Gorsuch seemed to agree, but also seemed to think there are some circumstances when non-party relief may be warranted. But how do you constrain that? The lawyer had no answer.
Roberts didn't say much on a specific remedy. But he's likely in the Gorsuch camp. Class actions and (what I'll call) unusual extraordinary circumstances.
Kagan and Barrett clearly think an injunction was appropriate in this particular case, so will probably join in the Roberts and Gorsuch line of thinking.
So that gets a mishmash of opinions, with at least 5 saying you can do with class actions. Potentially a new standard is put in place for the extraordinary situations, with a remand to district court to figure it all out. My personal belief is that the fifth circuits opinion that it must be one where the constitution demands uniformity across the nation is one to use. Such as a facial challenge to a statute/law that violates constitutional rights. (Like sotomayors gun example)
End result:
While nationwide injunctions do get reigned in, this will be a case where they are ultimately found to be okay either because class actions will quickly be filed or because this case meets any new factors the court may put out
Also remember this won't affect any administrative procedures act case which is where most every injunction against Trump comes from.