In a 2-1 decision, judges ruled that "the age-verification requirement is rationally related to the government's legitimate interest in preventing minors' access to pornography. Therefore, the age-verification requirement does not violate the First Amendment."

Haven't seen the opinion, but I'd think that the bar here is strict scrutiny, and that's probably a higher bar than being "rationally related".

https://en.wikipedia.org/wiki/Strict_scrutiny

In U.S. constitutional law, when a law infringes upon a fundamental constitutional right, the court may apply the strict scrutiny standard. Strict scrutiny holds the challenged law as presumptively invalid unless the government can demonstrate that the law or regulation is necessary to achieve a "compelling state interest". The government must also demonstrate that the law is "narrowly tailored" to achieve that compelling purpose, and that it uses the "least restrictive means" to achieve that purpose. Failure to meet this standard will result in striking the law as unconstitutional.

The standard is the highest and most stringent standard of judicial review and is part of the levels of judicial scrutiny that courts use to determine whether a constitutional right or principle should give way to the government's interest against observance of the principle. The lesser standards are rational basis review and exacting or intermediate scrutiny. These standards are applied to statutes and government action at all levels of government within the United States.

U.S. courts apply the strict scrutiny standard in two contexts:

• when a fundamental constitutional right is infringed, particularly those found in the Bill of Rights and those the court has deemed a fundamental right protected by the Due Process Clause or "liberty clause" of the 14th Amendment, or

reads article

Huh. Well, the majority opinion was apparently specifically that this was not the case:

The 5th Circuit, generally regarded as one of the most conservative appeals courts, found that the Texas porn-site law should be reviewed on the "rational-basis" standard and not under strict scrutiny.