I'm tempted to say that any idea which could change the political landscape even in potential is going to wind up controversial if it gains any substantial momentum, even if it's not at the moment. Politics is proverbially full of people with a vested interest in the status quo, who'd have obvious incentives not to be friendly to experimental governments; less proverbially, though, it's also full of people so attached to one shiny ideology or another that they're more than willing to preemptively demonize anything which looks like it might disprove it.

A competitive government project would probably be dismissed as the pet project of a bunch of idealistic cranks for the first few years of its existence, before it returns any substantial results, but I'd expect it to meet violent opposition if it ever starts looking like, say, modified Trotskyism, or modified Objectivism, or $BIZARREIDEOLOGYOFCHOICE might actually be a good idea in practice. The worst opposition would be directed at the experimental implementation of the idea, of course, but the system that facilitated it would also catch a lot of flak.