First of all you are confusing a state religion with a religious state, what the piece refers to is restoring the social kingship of Christ as it existed in the Middle Ages prior to the supremcy of the state in the social order.
Secondly, the differences are many and varied. You cannot compare the social kingship of Christ with a state dominated by an heretical religious doctrine such as Islam or even a denomination of Protestantism.
Of course such a thing as an Islamic theocracy leads to tyranny and atrocity, error begats error and evil begats evil.
I know what a "state religion" is - could you kindly explain what a "religious state" means, and why it is different?
Also, from what the article and you both have said, it seems to me that you want a country that is either 100% Catholic, and/or whose social foundation is Catholicism. Where would that leave the 75% of the US that isn't Catholic?
If I've misunderstood, forgive me.
"My kingdom is not of this world." - Christ the Only Mediator Between God and Man