There typically aren't criminal charges, but civil penalties for publishing private information do abound. Whether or not that constitutes censorship is a matter of semantics.
A newspaper? fined for publishing? no such animal.
You must be unaware of what happens when photos of minors are published without parental consent.
What happens, exactly? In the U.S., AFAIK, there is no law preventing taking and publishing photos in the newspaper of minors or others in public spaces without prior consent.
You can Google it, but school districts across the country have created bans on publishing pictures of students and those bans are enforceable by law.