The phrase "separation of church and state" does not appear in the U. S. constitution. Further, "separation of church and state" has come to mean different things to different people. More helpful is the actual statement of the first amendment: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof . . . ." That is, no religion (a word lacking clear definition, but hard to avoid in this context) is to be made the state religion. Also, that everyone should be able to hold to and practice the religion they choose.
May we then establish a non-religious belief? This is contrary to the free exercise clause. The first amendment singles out religion because established religion was the issue at the time, but that does not mean some other belief should be established in its place. This seems to be trading one bondage for another. Also, it is unclear why a religious person should consider this just.
How should a Christian look at this? One principle here is freedom of conscience. True Christianity is uncoerced, an act of genuine faith in God on the part of the individual (Hebrews 11:6). We cannot make people Christians by passing laws, which can compel outward observance but not change the heart. This is as likely to make them think themselves Christians when they are not or to rebel as to come to faith.
Also, whenever the church has been run by the state or tries to run the state, it has become corrupted. And because of this, it loses its ability to correct the state. Scripture gives examples of spiritual leaders who rebuked the misbehavior of rulers (2 Samuel 12:1-15; 1 Kings 17:1; 2 Chronicles 16:7-10; 20:37). This is difficult if the church and state are too closely identified.
But what a Christian should stand for is freedom to exercise his belief. This includes telling others about Christ (Matthew 28:18-20; Acts 1:8; 1 Peter 3:15). It also includes promoting justice in this world (Deuteronomy 16:18-20; Psalms 82:1-4; Proverbs 14:34). Now a Christian should do this in a loving manner (2 Timothy 2:24-26; Colossians 4:5,6), but we must do it even if it means choosing to obey God rather than men (Acts 5:29).
But often an act seen by one person as establishment of religion is another person's free exercise. This is made more difficult because many people on both sides are nitpickers. Perhaps both put too much importance on the issues involved. I am sure there is someone somewhere who was converted to Christianity by a school prayer or a Christmas creche, but I doubt it is a common occurrence. The idea that if we simply impose such things it will restore adherence to Christianity or Christian morals seems improbable. Therefore, while we need to stand for Biblical truth in a hostile culture, we must carefully pick the issues we support. We should oppose the establishment of non-religion, but not be caught up in a fight over trivia.