I'm not exactly sure what you asking in that Schaeffer's worldview was the same in terms of the civil magistrate as it was on every thing else. A worldview is a collection of presuppositions one uses to filter and interpret reality. They don't change from subject to subject. If you are asking what Schaeffer believed regarding the proper relationship between a Christian and the government, then that's exactly the subject of his book "A Christian Manifesto" - all 138 pages. A bit long to post here. If you want his detailed, very worked-out answer to just that question then read the book. I have. You took issues with DeMar's critique, so I ask, in your opinion, after reading Schaeffer, how did his worldview inform his view of the civil magistrate? What did his worldview tell him about the particular solutions to the problems facing our society, in particular the civil magistrate's role, as well as other societies?
"...so I ask, in your opinion, after reading Schaeffer, how did his worldview inform his view of the civil magistrate?"
And again I state that's a bit broad for a message board. The first response would be, "What aspect of government?" There are dozens, if not hundreds of particulars to this question, each of which require their own analysis. If I had to choose a sound bite summary, which is never wise, it would be "don't render unto Caesar what is rightfully God's."