...... However, I do hope that Roddenberry's vision of no organized religion, with religious figures in positions of authority and religious principles as foundations for secular laws (except in cases where such principles transcend individual religions, as in "You shall not commit murder") will come to pass. In fact, such developments have been underway in the West (at least outside the US) since the mid-20th century if not earlier.
....But yes, organized religion stripped of its previous power and influence does seem like a reasonable extrapolation, since as you mentioned, that trend's already underway in a lot of places.
Rodenberry's Trek basically says that humanity solved their major problems without religion whatsoever. It was all done by scientific discovery and hard work.
Thanks to technology, there is no hunger, need or want, so people now work to better themselves and the rest of humanity... you have to admit, this plan does sound pretty practical for an advanced society.
If anything, many episodes say that religion is the cause of the problems that humans tried so hard to get out of.
But the downside to this, is that the materialism seems to leave (at least humans) empty. Notice how various spirituality and religious themes keep popping up.
Whenever Picard, Sisko or other human characters are asked about what they believed in, they always gave a vague, awkward answer.
They needed something to believe in.