"The majority opinion was unsigned and consisted of a single long paragraph. It said the abortion providers who had challenged the law in an emergency application to the court..."

"... had not made their case in the face of 'complex and novel' procedural questions. The majority stressed that it was not ruling on the constitutionality of the Texas law and did not mean to limit 'procedurally proper challenges' to it."

From "Supreme Court, Breaking Silence, Won’t Block Texas Abortion Law/The law, which prohibits most abortions after six weeks and went into effect on Wednesday, was drafted by Texas lawmakers with the goal of frustrating efforts to challenge it in federal court" (NYT).

The "complex and novel" procedure — empowering random citizens to bring lawsuits against individuals — is a reason why getting early relief from this law is especially important. But it did make it hard to satisfy the traditional requirements for federal courts to act, which is exactly what the legislature meant to do. 

Usually, a lawsuit seeking to block a law because it is unconstitutional would name state officials as defendants. However, the Texas law... bars state officials from enforcing it and instead deputizes private individuals to sue anyone who performs the procedure or “aids and abets” it.... Plaintiffs, who do not need to live in Texas, have any connection to the abortion or show any injury from it, are entitled to $10,000 and their legal fees recovered if they win....

Here's the full opinion. There were 4 dissenters — the liberals plus Chief Justice Roberts. How did they get around the procedural problem (other than by sheer outrage at the aggressive attack on a well-established constitutional right)? The defendants in the case are — with one exception — state judges, who may, at some future time, have to deal with cases that may be filed under this new law. 

These judges are obligated (under the Supremacy Clause) to apply federal law, and they ought to dismiss any cases that are brought under the new law, because the law is, under current binding precedent, unconstitutional. For federal courts to enjoin state judges from enforcing the law, they would need to presume the state judges won't perform their duty as judges. 

The one exception — the defendant who is not a state court judge — is a person who swears he has no intention of filing any enforcement cases. To enjoin that one person wouldn't do much of anything to relieve the injury plaintiffs face. Other random citizens could still go forward, filing their enforcement cases in state court. 

In his dissenting opinion, the Chief Justice said the procedural problem was too difficult to resolve "without ordinary merits briefing and without oral argument": "I would accordingly preclude enforcement of S. B. 8 by the respondents to afford the District Court and the Court of Appeals the opportunity to consider the propriety of judicial action and preliminary relief pending consideration of the plaintiffs’ claims." 

Roberts avoids discussing the requirements for an injunction — notably the requirement of an irreparable injury that the stay will avoid — that were crucial to the majority. 

ADDED: There is also a dissenting opinion written by Justice Breyer, which the Chief Justice does not join, and this opinion doesn't take the procedural problem seriously:

I recognize that Texas’s law delegates the State’s power to prevent abortions not to one person (such as a district attorney) or to a few persons (such as a group of government officials or private citizens) but to any person. But I do not see why that fact should make a critical legal difference. That delegation still threatens to invade a constitutional right, and the coming into effect of that delegation still threatens imminent harm. 

Harm is threatened, but it must be threatened by these people that have been named defendants, and the relief requested must redress that harm.  To say "I do not see why that fact should make a critical legal difference" is to say I don't like these procedural requirements. You don't like the procedural requirements in the precedent and lots of people don't like the abortion right in the precedent. 

There are many, many cases where there are rights at stake and rights seem so much more important than procedure, but the procedural requirement is upheld — notably, Marbury v. Madison.

Breyer cites Marbury v. Madison, but for the point that rights require remedies (though Marbury had a right but no remedy):

Normally, where a legal right is “ ‘invaded,’ ” the law provides “ ‘a legal remedy by suit or action at law.’ ” Marbury v. Madison, 1 Cranch 137, 163 (1803) (quoting 3 W. Blackstone Commentaries *23). It should prove possible to apply procedures adequate to that task here....

It should... but he doesn't say how this lawsuit works that way. 

AND: There's also a dissenting opinion by Justice Sotomayor, also not joined by the Chief Justice:

[T]he State’s gambit worked. The structure of the State’s scheme, the Court reasons, raises “complex and novel antecedent procedural questions” that counsel against granting the application, ante, at 1, just as the State intended. This is untenable. It cannot be the case that a State can evade federal judicial scrutiny by outsourcing the enforcement of unconstitutional laws to its citizenry.

I agree with that sentiment but don't see the legal analysis of the requirements. Sotomayor does refer us to the District Court opinion, which she calls "thorough and well-reasoned opinion": 2021 WL 3821062, *8–*26 (WD Tex., Aug. 25, 2021). I haven't read that opinion, but if it is so well-reasoned, why didn't any of the dissenters tell us what the reasoning was? Just cut and paste the best paragraphs, why don't you?

MORE: I'm reading the district court opinion and hope to say something about it before the end of the day.