Being a Star Trek fan for more than 40 years, on one hand I admire their passion. On the other, I can't believe their naivete - if that's what it actually is. They would be far, far better off forming a movement to push proper funding for both taxpayer/NASA space and better incentives, prizes and tax benefits for private space: so as to accelerate new technologies including Propellant Depots, zero-boiloff cryogenic propulsion, nuclear-thermal, nuclear-electric and nuclear-plasma drives, total life support recycling, radiation shielding, efficient Heavy Lift and re-usable launchers and spacecraft, efficient artificial gravity solutions, advanced space medicine.....
I could go on! In short, all the 'Holy Grails' of exploration technology that will open up the Solar System - all the technologies and procedures that we know are wanted and needed, but in recent years have been deferred by endless budget cuts, lack of leadership and courage, 'Not Invented Here' etc etc.
With stable funding and leadership, and some risk-taking courage, we just might then attain a Space Exploration destiny that points the way toward the kind of wondrous 'Star Trek' like future that these folk are fantasizing about.
I would say to them: Do not pursue a sci-fi fantasy - pursue the glorious reality that is, as of today, just a few years and dollars beyond our reach. Build some real spaceships. Later on, call them whatever you like, Enterprise included. But don't shape it like the fantasy Starship - doing so would be a fetish at best.