The spirituality of integration is best expressed in Jesus' teaching of humility. A lot of people find it one of those code words, and it's exactly the reason they don't want to get anywhere near religion. Humility does not mean cringing or fawning before other people, which would just be another form of cowardice or plain weakness. And it's not manipulation, where one poses in order to gain control. At its heart, to be humble is to be humble before the facts of life.
Real believers approach reality carefully, modestly, to see and hear what is beyond.
It's both arrogant and ignorant to rule out something before you've explored it. To rule out the very existence of God, or to decide that God has nothing to do with real and everyday life, is the height of hubris. Some who are guilty of that are the sort of super-religious types Jesus criticized. But there are many others who say they aren't religious, but deny with religious fervor that there is anything more to life than what they know and what they can control. There's an old tale that helps relax this tension.