This law is a violation of 1st Amendment. Pure and simple. If I were IMDB, I wouldn't comply.
Note the law only applies if the person has a paid subscription to the site. That means the site has entered into a commercial contract with the person, and the rules then change somewhat. If IMDB wants to post ages or birthdates, the law doesn't stop them, as long as they don't accept money from the party in question. As soon as they accept money, their rights fall under contract law and are subject to other laws as set forth by statute. No one is forcing them to accept the person's money.
Think of it like a person rents an apartment. Before they rent, there is a big political sign on the apartment's windows, which the renter doesn't want on HIS window. Having a law saying the tenant can decide what, if any, information is posted on the window isn't a violation of the building owner's first amendment rights, since the contract has shifted aspects of control of the property. Having a law that says if you CHOOSE to offer a certain service, like the ability to modify information about you on a website, then other requirements also come into play, such as the ability to decide whether an age/birthdate are included, is permitted and isn't a violation of the First Amendment.