The only place I could see them running into trouble on that is if there wasn't a clear understanding of what constitutes "critical". Then, we'd have the same situation I talked about before - "void for vagueness". In order to have due process of law, you need a law. In order for it to count as a law, it has to have a discernible meaning. Otherwise, it would be a little more than a license for a public officer to rule by decree, which defeats the whole purpose. Other than that, I don't see any due-process violation in such a law.
Just out of curiosity, did Texas actually try to pass what you just described?
I'm not aware of Texas passing such a law, but there are some incumbent politicians who might like to if they thought they could get away with it. And recall that the Congress passed a similar law (the Sedition Act) less than a decade after the adoption of the First Amendment.
I think that your interpretation of the Fourteenth Amendment's due process clause is entirely legitimate. An interpretation that just imposes procedural (rather than substantive) requirements on states has a lot to be said for it. For one thing, it seems more democratic to allow states to write their substantive laws in the legislature rather than in the courts. One drawback is that once the Court lets the state legislatures know that they will be reviewing only their "procedural" laws and not their "substantive" laws, there will be times when state legislatures will try to fool them by dressing up and disguising some their more questionable procedural rules as substantive rules.
Note also that a Court which adopted your interpretation would not escape criticism from all sides. Since you would have to overrule Roe v. Wade and allow states to outlaw abortion, you might called be a fascist (at the least a sexist) by some in the pro-choice community. And since you would have to affirm the constitutional validity of any anti-gun laws that a state or local government might pass (because the Second Amendment does not directly limit state laws), you'd be hearing critical speeches from the NRA. And, for the same reason, of course, you would not have been able to join Rehnquist, Scalia, Thomas, O'Connor and Kennedy in utilizing "substantive due process" to declare unconstitutional (First Amendment) the New Jersey law which required the Boy Scouts to accept gay scout leaders. Your critics would then hold you ("and others of your ilk") directly and personally responsible for the breakdown and decline in our country's moral values.
That's the kind of thanks you'd get for your interpetation of the due process clause. And you thought that you were doing them a big favor, huh?
The unfortunate truth is that there is no interpretation that will be successful in avoiding public criticism. No matter how the Court chooses to interpret the due process clause, it will be criticized for "making the law rather than just applying the law like it's supposed to do."