Democracy vs. Theocracy

Recently I had a Twitter kerfuffle with youngish academically credentialed Calvinists active in conservative evangelicalism who advocated taking away the vote from women. In civil society, households rather than individuals should be represented, as they largely were before America ratified the 19th amendment guaranteeing women the right to vote. The heads of households are typically the husbands and fathers. One of these Calvinists also advocated a state church, to be determined by the local religious majority. Like others of this perspective, he denied that he is a theonomist but is simply a "magisterial Protestant." Others claim they are simply articulating "classical Protestant" teaching. After all, didn't the Protestant Reformers advocate for state churches and insist that civil magistrates must privilege and uphold Christian doctrine?