I wouldnt say that I have a right wing view of libertarianism, I've fully appraised all the political positions within libertarianism and found the whole deal wanting. While I could very possibly be described as a political and civil libertarian but I'm not really socially, morally or economically/fiscally libertarian, although I do believe that central planning and state paternalism are clumbsy means of economic regulation/management. The support for small or nightwatchman governments is a Minarchist, which can be either left or right wing in theory.
People dont mind their own business, if you want to take the example of this forum for instance it still requires moderation, there is a highly developed system of ignoring and shunning available, more developed than any social norm which presently operates or could operate in the abscence of coercive, intrusive and expensive legalism, but moderation is still required.
Now I take the point that anarchism is not the abscence of order but a highly orderly status quo but I dont see that happening, to be honest Bertrand Russell's maxism that law is preferable to the state of primitive anarchy which preceeds it makes sense. I dont know what the private alternatives to the state are, syndics? Nope, they'd likely act like crime families and the theory alone nor the efforts of organisers has been sufficient to call them into existence like business practices have created and maintained corporations.
Councils? Mutuality Clubs? Credit Unions? Clubs and Societies? All of the above? Well good but they havent threatened the state already so I dont see them doing it, not in event of an emergency, crisis or breakdown, plus I dont see quasi-political or social agencies like these succeeding were the economic ones havent because I see people are more economic in their existence than political or even social.
I generally dont invest in arguing with anarchists or anarchism or any of the paler libertarian socialist equivalents, if it motivates some good then all is well. To be honest I dont think there's enough personal responsibility anymore to make any of the classical political or economic ideas feasible, weather that's capitalism, socialism, liberalism, anarchism, neither are there anything like the norms of behaviour or organic, informal social structures which predated the rise of individualism and statism from the time of the American and French revolutions until now.