There's a difference between being for something and believing that you don't have the legal power to stop it, which is I believe Paul's feelings about state sodomy laws and similar.
Putin: "Libertarians want the government weak, selectively, when it comes to protecting against corporate abuse, so their rich capitalist masters can run the rest of us into the ground without any recourse. With everything else, they want the government strong and robust, especially at the state level, so they can harass leftists, gays, African-Americans and women with impunity. "
This simply isn't true, as even a cursory glance at any libertarian publication would tell you. Even the ridiculous paleo-libertarian Lewrockwell.com has a story on the front page right now about how America has wasted trillions of dollars on government spending and another about the state of North Carolina prosecuting the free speech of a food blogger.
Putin: "Paralyze government, make it do nothing, and then complain that government doesn't work well. That's the rightwing playbook right there."
See, here's the root of the your misconception, I think. You're looking at a very narrow slice of a broad intellectual movement, taking the most bizarre and extreme caricature of what that narrow slice thinks, and then expanding it to represent then whole. Libertarian doesn't mean rightwing, although I suppose a majority of libertarians who lean to one side of the political spectrum would be classified as rightwing. One of the fiercest critics of government overreach, one of the staunchest civil libertarians writing today, is Glenn Greenwald. It is inconceivable that anyone short of a communist could characterize him as rightwing.