This perspective may seem somewhat controversial. Was Apostolic authority from AD30 to AD70 an era of Apostolic authority that meant that Governing authority was actually Apostolic not Civil? hence it is controversial. For example, the apostles obeyed God not the Sanhedrin or Rome because of a specific Pentecostal anointing for that era.
This would mean that Romans 13 was about Apostolic authority. However, this opens up issues of theocracy, dominion theology, Kingdom Now. In reality, we live in the tension between the 'Already' and the 'Not Yet' of the Kingdom of God. It is already here but not in its fulness and won't be until Jesus returns.
So we need to always be working out how to engage with the culture in this tension between the already and the not yet of the Kingdom.
Abraham Kuypers notion of 'Sphere Sovereignty' is helpful here. Based on Genesis 1 and the law of 'after their kind' God put various creational spheres into creation to harness evil in a fallen world, like Male & Female as the Image of God, the family, education, business, the arts, in short the whole realm of human affairs is characeterised by creational structure and therefore will be oriented in a particular direction. The State is just one of those creational spheres but it cannot and must not overreach into other creational spheres in a dictortorial way because it will then damage the other spheres. Submisson to the State is based on an understanding of its creational structure and function to harness evil.
Moreover, the family came before the State in Genesis and is the basic building block of human civilisation. If the State changes God's creational structures by not acknowledging His creation, then there is basis for civil disobedience. The State therefore becomes a form of evil rather than harnessing evil.
The Pentecostal/Apostolic view is therefore if it can even be legitimised is for a specific period only.