I had left another comment here which hasn't gotten published (perhaps it was too long). I just want to add that at least in the Eastern context, the "spiritual but not religious" movement does not have much to do with a modern scientific intelligence (though it is at least partly related to it), but more to do with the idea that living spiritual experiences trump religious texts and creeds, and the inner conviction that the Divine is too vast, tremendous and infinite to ever be contained in any one religion, text, set of rituals, or creeds.
As my teacher Sri Aurobindo once put it, responding to the fears of a religionist in moving away from traditional religionism: "Thou mayst be deceived, wilt thou say, it may not be God’s voice leading thee? Yet do I know that He abandons not those who have trusted Him even ignorantly, yet have I found that He leads wisely & lovingly even when He seems to deceive utterly, yet would I rather fall into the snare of the living God than be saved by trust in a dead formulary."
More information about text formats