Technically, Cato, is a classical liberal libertarian institution favoring small government, and the civil society. (Cato does work within the system and has an audience in DC because it works within the system.) The Heritage group also favors traditional society and classical liberalism. The majority of the remaining think tanks (FEI, etc) place more emphasis on economic policy and less on social (normative) rules.  Only the Mises Institute and its network advocates anarchism, and the Property and Freedom Society advocates private government. The Mises Institute takes advantage of the rabidly autistic male population seeking social connection on the internet, which gives them disproportionate presence relative to their nominal if not negative influence on policy and thought. https://www.quora.com/Is-the-Cato-Institute-libertarian-in-political-views-How