I'm not so concerned about governing with Christians... after all, somebody has to keep 'em in check, or else they may cease to behave like Christians and turn instead into fascists. : )
1st Am. "...shall make no law respecting an establishment of religion..." and such pretty much supports the point I make.
If this were specifically meant to be a Christian nation, I think it would have been spelled out.
I cannot explain intelligently any rebuff to your specific point. What I will do is this:
I'll add another wrong to the pile of wrongs that existed before and when our country was founded. Christian-only government is a wrong in a society which was supposedly set up to be a republic / representative semi-democracy. Some people will not be represented if they are not Christians. So the hypocrisy is apparent. The lie of a Constitutional Republic not being what it has been claimed to be.
Another wrong which was acceptable upon the Founding: slavery.
Guess what: If Christians had single-handedly created this country and all that it is to this point, fine, perhaps the rest of us can just step off; however, as soon as others contribute--BAM! Now all contributors must be included.
What would the Founders do?