Translation
However, if anyone chooses to ignore [these matters], let him be ignored.
Paraphrase
However, if someone still chooses to not recognize that these matters are God-ordained, you should not recognize him or what he says.
HERE IS THE CONSEQUENCE PAUL RECOMMENDED
In this verse Paul says that we should not wait for the negative consequences of disrespecting authority to begin to reveal themselves (which can sometimes take a generation), rather we should assign consequences to people who do not want to follow the standards God has established for authority structures. In this case the consequence was that such a person should be ignored. No one should follow that person’s attempts at leading others. Leadership can be described this way: Look behind you; if people are following you, then you are a leader (whether you want to be one or not). The disrespectful person may think of himself as a leader and may claim the right to leadership, But he does not deserve to lead for his disrespect has caused him to lose the moral authority needed to lead. Therefore, if he ever turns around to take an honest look at reality, he should find that no one is following him.