There are always "new spiritual insights," if you mean those not familiar or known to you, me, or others. But, more profoundly, do any really "new spiritual insights" exist in the cosmos?
This is a profound question, as the cosmos is always changing and evolving under the direction of Love, often acting through universal law (including karma). Since God is also always changing, as Lovexpression, there is no reason to suppose that the cosmic Mind (God) cannot also create new spiritual or cosmic insights. Indeed, She has an infinite ability, a bottomless reservoir, that makes this not only possible, but probably inevitable.
The Mind is always dreaming, and always dreaming up new beings, worlds, and even universes. Therefore, it would be antiprogressive to believe in any "static" truth, as truth is reality, and reality is more often like a fluid than a solid. It is, in fact, one of the major challenges of the mystical (enlightened) mind to approach a state of semi-fluidity, flexibility, and adaptation in order to keep pace with the cosmos.
If we allow our minds to become like bricks, then, we are caught in paralysis and petrification; we have stopped growing. Knowledge, especially in its manifestation as gnosis, is not a finite reality, but a limitless one. So, new concepts and ideas are always coming into being, and some, no doubt, represent "new truths" (realities).
Fundies are terrified by this mutable and mutating cosmos. They like to have everything "locked down," everything in nice, orderly but finite little categories like Pez pellets lined up in a dispenser. While this might seem to be "neater," or even "more orderly," this is not compatible with an infinite universe existing within a bottomless and breath-taking Mind.