I think mysticism is no less prevalent today than it was 1000, 2000, or 3000 years ago.
Hold "religion" aside entirely for a moment, there's herbal supplements, essential oils, PETA, some sects of environmentalism, etc.
And we bandy the word science around, but I'm reasonably certain that among some, there's a thoroughly unscientific worship of science. If "science" says something is true, they accept it blindly. Of course, it's simply not possible, nor profitable, to individually retest every one of those little assumptions in life we accept as fact.
That's because nobody considers scientific theory to be infallible. If it turns out something is wrong, say Einstein's theory of relativity, then we'll adjust. But we continue to seek new information. And we at least have something to go on. Something we can test -- again and again if needed.
Can test again and again, yes. But so frequently don't. In nearly every case, science says "we're pretty sure this conclusion is true, given this evidence." And yet, given the evidence, individual conclusions could vary widely. Given the training and background of each individual, when presented with the experimental results, wildly different conclusions may be drawn. Reproducible results don't necessarily produce scientific fact.
And, in fact, I think between Einstein and Heisenberg, probably Planck as well, it's pretty much guaranteed that there's a point where we'll have to say "this is how we've seen it work in 100,000 times out of 100,000, and that's the best we can do." Because it simply won't be possible to experimentally determine underlying behavior. But everyone will accept it as scientific fact.
At some level, "science" has its own cult, with its own worldview. Its own "priests" who understand the "doctrine", and the lay people who accept the precepts on faith.