When historic Two Kingdom (2K) theology was developed it was developed so as to keep the Pagan state from overstepping their bounds as it pertained to Church matters. So, for example, the Church reminded Charles I (I might have the King wrong… going from memory) that when it came to matters of the Church he was merely a member in the Church like the rest of the members. He had no Jurisdiction over Church affairs as King.
However, what Radical Two Kingdom (R2K) has done is to flip this arrangement. What R2K “theology” does is that it keeps the Church from influencing the pagan State, going so far as to suggest that the Church doesn’t have a role in speaking a “thus saith the Lord,” to the Magistrates in what it calls “the common realm.”
Whereas original 2K was concerned with protecting the Christian Church from pagan influence, R2K is concerned with protecting the pagan State from Christian influence.
I don’t think one needs historic 2k as much when the whole social order is shaped by the Christian ethos. It just wouldn’t be an issue where the State and the Church are both expressly Christian. However, for the times when either Church or State went haywire 2k allows the Christian Church as against the pagan State or the Christian state as against a apostate Church to exercise a godly interposition.