"Would this not mean that our notions of God, honor, love, justice, the spirit world, and all things unseen and imperceivable are mere mental constructs?"
Should we be prejudiced against, exclude a priori, such a discovery?
EVERYTHING is a mental construct. With no human nervous system, there is no human.
In Vedantic and other Eastern cosmologies, there is the idea that the world as we see is "maya", an illusory reality, while "Reality" remains mostly unknown. And each human's goal is self-Realization and then Self-Realization so the true Reality can be perceived directly. And self-realization requires purifying and refining the body and nervous system so it can perceive Reality correctly. And weak echo of this is the Greek ideal of "a sound mind in a sound body". Is the universal practice of altering consciousness by consuming chemicals to acheive a different consciousness nothing but a desire by the nervous system to escape reality, or perceive reality differently?
An analogy would be someone saying Newtonian physics is all there is. But Newtonian physics, for all its grandeur and power, was only a tiny, myopic view compared to the more "real", and much more powerful, quantum physics.
So your PS is that Atran is suspect or unworthy of attention because 1) he's not a Bible-thumping Christian evangelical on your side and 2) the hated NYTimes wrote an article about him?
I get the impression that Atran is a more serious thinker and searcher for truth ("Truth"?) than people who consume the packaged pablum harangued at them by "Christian" "ministers".