This trend is visible in more than Islamic poetry: any spirituality that is not "secular" is seen as suspect and potential brainwashing. One can also see this kind of effect in "secular buddhism", which is presented as "the true message of the Buddha, with the archaic cultural baggage of antique India removed" - which forces to jump through some hoops, as the goal of Buddhism itself (ending rebirth) is seen as cultural baggage. Unfortunately, more often than not, it is just a way to avoid questioning one's own preconceptions and cultural baggage - that everything is "obviously" reducible to matter, that consciousness is "obviously" produced by physical processes in the brain...

Interestingly this is a theme one can find in Soufi literature: in the Conference of the Birds, from Persian author, and precursor to Rumi, Farid Ud-din Attar, there is the story of Archangel Gabriel seeing Allah deeply absorbed in listening to the prayer of a human. But when Gabriel searches, he cannot find who is this saint. Only when he finally searches outside of the Muslim world does he see that the prayer comes from an "Image Worshiper" (a sin in Islamic doctrine). What I get from this fable is that though the author recognizes the possibility for a human not exposed to the "true religion" to be of spiritual value, it can only happen if this human has a strong religious attitude of worship, prayer and devotion - he might pray to the "wrong" god, but with the right attitude. Which is kind of the opposite of taking out the religious elements - you might replace Allah by "the One" or "God" if this helps you resonate, but not dilute it in a vague formula such as "that which is good" or similar examples as described in the article.