The debate is particularly significant in a pluralistic, constitutional republic (such as the U.S.), where there are competing belief systems under a common political umbrella. The consequence of mixing Christianity with politics in such a system is an inevitable watering down of core Christian beliefs.
A fine example of this can be found in the arguments made to the Supreme Court on the meaning of "under God" in the pledge of allegiance. Those supporting the retention of the phrase argued in no uncertain terms that "under God" was an innocuous, and effectively meaningless, phrase that had no religious significance or connotation. By this argument, "under God" was reduced to a cultural catch phrase similar to "have a nice day."
This marginalizing of God for minor (and meaningless) political gain inevitably finds its way into the Church itself - leading to precisely the problems addressed in the article above.
Finally, somebody who has read the New Testament.
Anybody who thinks America can become more or less "Christian" by political action or by arguing over moral or cultural issues has YET to understand the Jesus of the gospels. It can't possibly be more clear that:
1. Jesus had NO interest in influencing politics
2. Jesus had NO interest in discussions of moral issues, per se, in isolation from a relationship with Himself. He made occasional comments, but the thrust of his work was invariably to teach people how to live in something He called "the kingdom", which He explicitly said was "not of this world".
3. Jesus had NO interest in reforming society by any method other than a personal devotion to His person and His utterances.
It was His scandalous LACK OF INTEREST in politics and wider culture (plus other things) that got Him in trouble.
The Jesus of the gospels is still a stumbling block to people who think Christians and churches have ANY mandate OTHER than to go into the world and teach individuals to individually respond to Jesus. Anything else has always failed and will fail. Anything else is a distraction from the gospel and is, then, a false gospel.
To the degree that "Christianity" is losing its influence on Western culture, it is simply and solely because there is a great falling away on the part of individual "Christians".
"Political non-involvement" seems to be one of the authors' bad things to be. I can't imagine how anybody could read the New Testament and find ANYTHING OTHER than a clear, willful, systematic, proud "political non-involvement" on the part of Jesus and His followers.