Across most of history religion was integral to the polis; to what we call today “political affairs”. It is only in the protestant west during the last 2 or 3 hundred years that protestant intellectuals have advocated separation of church and “state”. During the founding of the USA there were huge debates about “disestablishment” or whether each state would choose its own “established” church/religion. Inspired by the atheism of the French revolution Jeffersonian radicals in the USA won the debate over religion in the public sphere and so “separation of church and state” became settled constitutional doctrine in the USA.
The separation doctrine has never really worked that well because human beings are largely religious creatures. They don’t like leaving their religion behind when they enter the public sphere. The history of political conflicts within the USA since the founding has largely been fueled by intrusions of religion into politics. there would have been no civil war and no abolition of slavery without the abolitionist religious fanatics to cite just one example.
The only reason why the separation has SEEMED to work well for the USA in the last 200 years is because the only religions the state has had to deal with are the emasculated form of Christianity (i.e. protestantism); and a protestantizing form of catholicism (the “Americanist” heresy gained allegiance from most of the catholic bishops throughout the 20th century. Americanism was given new life by Vatican II and by similar anti-catholic trends in Europe in the 20th century.
These two forms of Christianity do not threaten the state as they are inherently statist themselves. When a religion casts away its identity markers such as distinctive dress, distinctive liturgical ceremonies, public processions, a distinctive calendar of commemorative days, religiously homogenous ghettos, neighborhoods or communities and so on …in short when a religion forfeits culture to the state the state has won and the religion will accommodate to the state’s liturgical feasts, the states commemorative calendar, the state’s values etc.
The separation doctrine, however, is on its last legs. It cannot survive the 21st century. Unlike the emasculated forms of Christianity that have existed in America until now Islam cannot and will not be assimilated into the modern state. Similarly the the left wing of the Catholic church which is the main supporter of the Americanist heresy is on its way out seeing its last gasp in the papacy of Pope Francis. In Europe and in Russia orthodox brands of religion are on the rise. You do not need whole populations to adopt orthodoxy for the orthodox to win. You only need a dedicated few like St Francis of Assisi who along with St Dominic largely saved the church in the 12 century just as St Ignatius and the jesuits saved the church after the reformation nearly destroyed it in the 16th and 17th centuries and St Benedict did after the fall of Rome and the dawn of the dark ages. It is the saints who save the church but saints who are also leaders who can organize and inspire other men with zeal.