... there is no such thing as a non-religious experience...
LOL, steady! I would have thought only if the term 'religion' is reduced to the anodyne can that statement be made. I would have thought what determines the experience as 'religious' or not is the religious sensibility of the experiencer. Two people can delight in the same thing, one sees through the veil, one sees the surface ... one is a religious experience, one isn't.
And I think many atheists would take issue with the idea that all experience is religious experience!
Too often it is thought that a religious experience must be something dramatic and profound.
Oh agreed, but I think that's the product of 'consumerism in the West, especially in the US where religious freedom allows for commercial marketing. A surprising number of American denominations started life as commercial enterprises. In the post-hippy west, we have the like of Campbell's 'follow your bliss', etc.
Authentic 'religious experience' is utterly profound, but often un-dramatic. As the Zen say, 'before Enlightenment ... after Enlightenment ...' nothing appears to have changed, but the cosmos has shifted on its axis. It's contemporary consumers who chase 'religious experience' in much the same way they'd pursue any novel sensation. If you listen to the commentaries of the Traditions, they all point to 'the dramatic' as being the ego, the individual psyche, nothing more. It's those who want a bang for their buck who're looking for 'experience'.
But with an ultimate basis of reality ...
That rather depends where one determines the ultimate basis according to one's ontology. I'd say for the religious, whatever 'It' is, is the ultimate basis of reality. For others, atheists or those into scientism, it's the parameters of physics.
The skewed science debate is four-square in the empirical, if it cannot be empirically determined, it cannot be, and the corollary of that is that one day science will explain all religious phenomena ... again the product of materialism/consumerism which dominates the West.
I like how Paul Tillich described the religious content of people, places, events, things, etc. as those things that are transparent to the divine.
I would agree, but there are those whose vision is opaque or occluded.
Now this transparency is often felt in moving things like art, music, nature, literature, relationships, etc...
The religionist would discern between the transparency of the transcendent, or the transparency of the ego. Many claim to experience 'It', when actually they're experiencing themselves. This problem is highlighted when such people gather a following, their ego-myth becomes a self-perpetuation and self affirming mythology ...
... but I believe everything including the evil in the world says something about the divine dynamic in the creation and activity of reality.
Hmmm. Depends how. The determination of 'evil' is, in that sense, measured against the Divine, but is not a product of the Divine. The divine determines what is evil, and we have appropriated that term for ourselves ... so yes, but the Divine is not the source or cause of evil, if we're talking western notions of divinity, unless the divine is 'mad or bad', to paraphrase C.S. Lewis.