For the Lord’s sake subject yourselves to every human creation, whether to a king as being superior or to governors as sent by him to punish wrongdoers but to praise those who do good. For it is the will of God that by doing good you may silence the ignorant talk of unreasonable men.
The governors are wanting to punish wrongdoers. This isn't persecution, allowing them to do that is part of being in subjection to superior authorities. If you're not being praised for doing good and silencing ignoring talk, you're doing it wrong.