"Y'know what the real tragedy of the blues is, man? The way they're takin' it away from the people who perfected it, the corporate record labels, and sellin' it down the river to these teachers-union parasites who wanna force-feed it to kids in public school musiic classes".
Joking aside, if things in the overall culture had gone a little(well, okay, considerably) differently, you might have seen the counterculture embrace a decentralized approach to governance, with a back-to-the-land ethos that's hostile to federal encroachment in the areas of education(because "the man" can't force his values on our kids), and also to things like highway construction(along with the more expected opposition to conscription, drug laws and morality police). This might spread over into opposition to the welfare-state as just another cudgel wielded by the tyrannical government.
But, in all honesty, it was the general trend of liberalism in the mid-to-late twentieth century that individualism in the sphere of personal regulation got melded(sometimes awkwardly) with increased regulation in the economic sphere. That was all around the world, not just in the USA and Europe, so it was probably inevitable that the it would manifest itself in the counterculture as well. Commune-dwelling hippies might not have liked the government building big dams near their bucolic communities, but at the end of the day, they'd probably like the plans of the big oil companies a lot less, and would look to the government to block them. Same basic dynamic with issues like civil-rights etc.