An an anarchist, I approach modern secular theocracy, or state-worship, in the same way that an atheist might have approached traditional theocracy in the period before church and state were separated. For instance, let’s say that the sectarian warfare between Catholics and Lutherans that occurred in the early modern period was still going on.
Today, in the United States, we might rotate the presidency between Catholics and Lutherans every 8 years or so, with the current President being some kind of buffoonish Pope. Catholics might control the Senate with Lutherans controlling the House, with a Catholic majority and Lutheran minority on the Supreme Court. Some states would have Catholic governments, some would have Lutheran governments, and some would have divided governments. The large cities and heavily populated areas would be dominated by Lutherans.
Meanwhile, both Catholic and Lutheran clerics would be issuing edicts claiming to be oppressed because Pope was constantly insulting Lutherans and the Lutheran media was constantly ridiculing the Pope. Meanwhile, atheists and out of power religious communities (Jews, Muslims, pagans, Anabaptists and other radical Protestants) would recognize the Catholic/Lutheran conflict as the battle between rival gangs of tyrants that it is. And there would probably be “Muslim Catholics” or “Jewish Lutherans” who might hinge their bets on one or the other side in hopes of acquiring some slight advantage for themselves.
There would likely be Catholic yahoos among the peasants who professed undying allegiance to the Pope, and there would likely be “Lutheran Justice Warriors” claiming to be oppressed by icons of Catholic saints.
And then there would be atheists like me who sit back and laugh at it all.