That is as it should be. But it is far from many in this nation who favor Christianity as an official religious philosophy. There are quite a few here on this forum who favor a theocracy here. I am referring both to Catholics as well as other Christians.
That is one of the many differences between Christianity and Islam. Even in Islamic states that are not radically jihadist, Christians often are persecuted. There is no inner rebirth in Islam, no personal conversion. It is a religion of works, of physical acts of obedience. Therefore there is no real reason why they shouldn't use government to force this obedience. That is why democracy has such a hard time over there.
I understand the differences you are painting between the two, and right now they are as you have said, but history shows how any religious ideology can move into the political spectrum if permitted. Just look at the Church of Rome in the Crusades, the Holy Roman Empire, France, Spain, the Inquisitions. Christianity is now and should be as you say a very personal thing. But the separation of Church and State philosophy was created to prevent the kinds of things that can happen when religious ideologues get in control.
The first step in that slippery slope is for religious tests of any kind for our justices or any other government official. Once you permit that, you are placing Christianity (or some other religion) in a policy-making position.
I've been on this fourm awhile, and I don't see the calls for theocracy as you do. I'll tell you what I think. I would like to see Christianity, through the democratic process of the grassroots voting their preferences, be the predominant ethic in our culture including our government.
This will take a lot of evangelism, and a lot of work. But our nation was overwhelmingly Christian when it was founded, and it was more free that anywhere on earth. Today it is less Christian that in has ever been, and is now less free and more socialistic. I believe there is a causal relationship here.
But politics aside, Christianity starts with a person acknowledging their sinful nature before God. Christ came to forgive and to heal. Government has no part in that other than to get out of the way.