What's the problem? This isn't the first place in the country that has banned vulgar t-shirts.

It doesn't violate the First Amendment. Where were you when public intoxication was outlawed? Isn't that, like, violating your right to speak your mind and be who you are? Nope. This sums it up pretty well:

The right to free speech is protected under the First Amendment of the United States Constitution. A statute is deemed to be overly broad and violative of the Constitution if it prohibits speech that is merely offensive to certain persons. The prohibited speech must constitute "fighting words," which are defined as words that have a direct tendency to cause acts of violence by the person to whom the words are directed. Fighting words include profane, obscene, and threatening words.