In most cases, yes. Most states consider shopping malls to be the private property of the mall owner. Just as with any piece of private property, owners can make rules regarding that property, including what is appropriate attire; think of “No shirt, no shoes, no service.”
In 1976, the U.S. Supreme Court decided the case Hudgens v. National Labor Relations Board. This case involved a group of labor union members who were picketing inside a privately owned mall. The union members filed suit claiming, in part, that their First Amendment free-speech rights had been violated after they were asked to leave the premises or be arrested for criminal trespass. The court looked at past cases and found that the First Amendment does not prevent a property owner from restricting the exercise of free speech on private property, in this instance the shopping mall. So, for example, if a mall shopper were asked to cover a shirt that the mall owners found to be offensive, the shopper would have to comply or leave.
New Jersey and California have found their state constitutions to provide more freedoms than the U.S. Constitution — meaning that in these states constitutional rights to free speech can prevail over the private-property interests of mall owners. See Pruneyard Shopping Center v. Robins (1980). However, most states that have addressed this issue have found in favor of property owners.