But do humans crave order more or do they shun it? I think humanity seeks its own self-order on its own terms and doesn't like being pushed around by "higher beings" who think they know better. This existential question was effectively discussed in Babylon 5, contrasting the difference between the Vorlon "order" philosophy, involving the influencing of lesser sentient life by a super-race and the Shadow "free range" Darwinian philosophy of letting the lesser sentient beings figure the universe out for themselves, where only the strong survive. Interestingly, I found myself quietly rooting for the Shadows towards the end. Vorlons actively manipulated the other races by appearing as gods and blatantly directing their development against their will, ostensibly for our own good. That didn't sit well with me philosophically. Smashing worlds with their planet killer when they realized that nobody wanted their flavor of control kind of sealed the deal. They had their little scorch-and-burn tantrum and decided to cleanse the entire galaxy of us puny sacks of water and chemicals and hope that new, more easily-controlled life will evolve once again in another billion years for them to play with. Trelaine would have gotten along well with them.
Getting back to the original Trek question, I'm not entirely sure that that's the Q's motive. JirinPanthosa makes a good point that the Q potentially saw humanoid life - particularly human life - as a clear and present danger in the far future to their own existence. I think Q was actually sent to "check us out" to see what kind of threat we posed. If they were truly omnipotent, they would have seen into any number of possible futures what we could become but I think they couldn't nail it down, frustrating them. Picard's Shakespearean "in apprehension, how like a god" speech particularly incensed Q and I think struck a BIG nerve, exacerbating the frustration. If any of these super-races wanted to impose some kind of order, it was the Organians and maybe the Metrons, but the former appear to have checked-out somewhere along the way in the late 23rd and the latter never seemed to care much about anything outside the Gorn region of space. The rest of the other big races clearly have more important things to do with their non-linear time than play with the galactic ant farm.
I personally prefer the TOS Battlestar Galactica philosophy as employed by the "Ship of Lights" beings, which were allegedly ascended Lords of Kobol. They sought to gently nudge humanity along without actively interfering in its natural development. It was only when Iblis attempted to directly manipulate the humans (imposing his own form of "order" - I detect a pattern here) that they decided to actively intervene and reveal their existence to re-balance the grand cosmic chess game. They mentioned to Apollo & Starbuck, "As you are now, we once were; as we are now, you may become", stating that they encourage the ascension of humanity to a higher level of being, but they will largely be on their own, with some help and occasional guidance from the Beings of Light. Arguably, a better compromise between the more inflexibly absolutist Vorlon and Shadow doctrines.
In short... Can the Q be stopped? Almost certainly. Should the Q be stopped? Probably. Humanity might pose a threat to them, but they definitely pose a threat to us.