So if NJ wanted to ban a church or a newspaper, that would be permissible?
The 1st Amendment has been incorporated against the states. They cannot ban a church or a newspaper in violation of the 1st Amendment.
The 2nd Amendment has not been incorporated against the states. States can regulate ownership as guns how they see fit. Only the Federal government has to comply with the 2nd Amendment.
A case to incorporate the 2nd Amendment against the states is on the Supreme Court docket this term.