As a non-religious person, I have to say this notion that humanity is secular in the future is wrong. There are plenty of examples of humans still practicing religions, even in the 24th century, despite Picard's claim to the contrary. Christianity in particular is definitely still around, we see a church on TNG in Sub Rosa, and people make the sign of the cross in that same episode. On DS9 Kassidy Yates mentions her mother is a practicing Christian. It's also clear Native Americans still practice their spiritual beliefs in the future, and Hindu holidays are observed on the Enterprise D. Prior to the 24th century, Kirk himself admitted to worshipping a god, and Dr. Phlox mentioned plenty of religious practices rituals and services while on Earth.
So really, it's only Picard who seems to think future humanity is secular, with plenty of evidence to the contrary. Hmm, Picard is the only one who definitively refers to the Prime Universe's Federation Starfleet as non-military. I'm beginning to think he might actually be a delusional individual.