I think a belief system is associated with spirituality. Though unexplained things can be guessed in science. It is guessed utilizing facts. I would say it is more of a prediction or forecast.
Science predicts and test.
Spirituality believes and asserts.
It seems people who believe that "science is spiritual" are people who believe in theoretical physics to the point of accepting them as absolute truths or laws. They seem to not realize the uncertainty of theory or hypothesis. They seem to not understand what science is.
Science is not spiritual. As spirituality contradict
