Now the church and the state are separate entities
Just like back then when its founding fathers designed it that way.
For example, Hillary Clinton has no authority to administer the Sacraments; and a pastor has no authority to raise a federal army and declare war.
Because it would be unacceptable. Another important principle is the separation of powers. This also means that the president is not an emperor, also intended that way by the founders. The lessons were learned from Europe's problems and European countries too were progressing away from savagery, total corruption and heretic divinized authorities.
there is absolutely nothing wrong with a State official acknowledging the authority and the Word of God in the civil affairs of men
In their personal life? Right. For state worship? Moses would break the tablets if he saw your fake god.
No State action or law is valid unless it conforms to God’s law and His Will
Nonsense. Noone knows what those would be anyway. Crackpots like you claiming to know is not different. That's why there were older gods and religions than yours, that there are many religions and that your own religion is rife with sectarianism. It's much safer for your redemption to pray in private, hoping to be forgiven for your sins, than to be complicit in forcing your misconceptions, sins and hypocrisy on everybody, or to justify your crimes when speaking for God.
“The Laws of Nature and of Nature’s God”
Where do you see that in the founding father's constitution? How would anyone know this and be sure to get it right anyway? For instance, creationists reject actual laws and facts of nature discovered by science in favor of ancient ignorant human mythology. Patriarchs trying to enforce their ideological views against nature falsely pretend that what exists in nature that they want to suppress violates nature. They're obviously ignorant of nature, or against it.
Therefore, prayer, Bible reading, and biblical influence in civil government are entirely American and perfectly legal. As a matter of fact, our Founders encouraged it!
Encouraged that you be able to practice your faith in church and at home? Yes. To impose it via the government? You're lying and it's actually very clear that they wanted to make sure that government could not hire on the basis of religion.
Why should we trust a liar who speaks for not only God but for the founding fathers and promotes pseudohistory? Could it be that because you cannot be trusted and are wrong, is the reason that you'd like to be able to dictate? Because people see your deception and will not blindly accept your rule and false justifications. Who's the father of lies, hypocrite?