There is a good and generally beneficial kind of civil religion, which acknowledges that we are "under God" (or god) and that that god will hold us accountable for what we do, especially if we hold public office
But there are many bad kinds of civil religion: suggesting that God is on your side and therefore you are right, rather than finding out what God commands and being on God's "side;"
mixing the Gospel with a nation's laws or pretending Jesus affirms the specific form of your political policies; putting all one's hopes of national good and well-being into the election of this or that candidate (all idols fail);
trying to remake the United States as either an Old Testament theocracy, or a New Testament one;
thinking that any past or future form of administering laws has anything to do with Christianity whatsoever (e.g., "this used to be a Christian nation" or "doesn't Jesus say we should...?")
Christianity has to do with revelation, the Holy Trinity, Jesus and his death and resurrection, forgiveness, Baptism, Holy Communion, etc. The State at all times and places has to do with reason, laws, coercion, and power.
It does not matter who has the civil authority; Jesus is very clear to his apostles: it shall not be so among you. Whatever you think is good or bad about a president or other governmental authorities, leave actual Christianity out of it.
The Church is not and should not be the State; the State is not and should not be the Church. If you are a Christian, be one. Believe God in Christ and love and serve your neighbor.
If the president claims to be a Christian, he or she ought to be one too, and it is right to hold those in authority to their claimed confessions, and to remind them that they will be held accountable for what they do since God put them there
But the Gospel of Jesus Christ (the forgiveness of sins purchased by his blood and death and given to us in the ways he has chosen to do so) is irreconcilable in this age with the exercise of the government under law and reason
They are both God's now and finally, but he rules differently in each, and they will not be seen to be one until all things are under the feet of Christ, he delivers all things to the Father, and God is all in all.