At least in the Eastern context, "spiritual but not religious" is not something entirely new. The Bengali renaissance of the 19th century was a major reform movement in Hinduism that sought to separate actual living and transformative spiritual experiences from organized religion with its creeds, rituals and dogmas.
I think this idea is perhaps partly related to modern scientific intelligence, but it has more to do with the inner conviction that the Divine is too vast and infinite to be restricted to any one religion, text, creed, or code of ethics. I leave you with a poem from Swami Vivekananda, one of the Hindu reformers from the 19th century:
THE LIVING GOD
He who is in you and outside you,Who works through all hands,Who walks on all feet,Whose body are all ye,Him worship, and break all other idols!
He who is at once the high and low,The sinner and the saint,Both God and worm,Him worship — visible, knowable, real, omnipresent,Break all other idols!
In whom is neither past lifeNor future birth nor death,In whom we always have beenAnd always shall be one,Him worship. Break all other idols!
Ye fools! who neglect the living God,And His infinite reflections with which the world is full.
While ye run after imaginary shadows,That lead alone to fights and quarrels,Him worship, the only visible!Break all other idols!
(Written to an American friend from Almora, 9th July 1897.)
— Swami Vivekananda
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