It is a nation based on Judeo/Christian principles and at the core is that we are free to believe what we want without government interference. Sadly it does it all the time, and others who see someone holding a "John 3:16" sign at a football game sue the stadium to have those kind of signs not be held (Kountze, Texas).
The neutral is there, I do not see where your issue is on it NOT being neutral. As for Christian displays on government property, that has always been allowed. If you supply the stuff and put it up within safety and such guidelines there should be no problem. Heck, they used to hold Church services in the House and had military bands play the worship songs. So asking to put up a nativity scene should not be a big deal.