There is no absolute right to free speech as has been ruled again and again and again. Restricting access to pornography to adults is one of the areas that has been ruled as an allowable restriction, or more accurately there are laws against providing children with pornography, just like there are laws restricting access to alcohol and tobacco. The interesting argument in this case is, can the state require a specific mechanism of restriction be employed. Looked at another way, would the case hold up if instead of porn we were talking about alcohol? If Texas required a site selling wine for instance to maintain a database of customers state IDs would that be legal? I suspect the answer would be yes, but it's debatable, so it's risky to bring a lawsuit with that as its sole basis.

The warning on the other hand, that's a MUCH stronger argument. More so even than censoring speech, compelling speech is looked down on far more severely. The law is asserting as facts, things that at best are debatable, and at worst are just downright lies, and forcing sites to repeat those dubious "facts" is really not going to go over well. They are so bad in fact as to verge in libel. Focusing on the warning label is a pretty easy slam dunk in their case, while going after the ID portion is much more iffy. I don't think they'll be successful in getting the law overturned on the basis of the ID collection, but I do think they'll succeed on the basis of the required warning label.