You write: “Rand Paul pushes this neo-anarchist belief that the government should get out of everything,”
We anarchists don’t believe that “government should get out of everything.” We believe that government should cease to exist, and take capitalism, racism, patriarchy, and all other forms of class oppression straight to hell with it. Rand Paul is as much of an anarchist as any other “limited government” conservative Republican, which is to say, not at all: he wants to trim some parts of government here and there, while leaving in place all the violent functions of government that prop up existing forms of oppression (in particular government militaries, government police, government prisons, and government borders; he is especially fond of government border laws and using government to attack Latino immigrants). Anarchism is an entirely different, far more radical proposition.
You write: “… including mine safety because ‘who would work at an unsafe mine?’ Well, the people who have two choices- an unsafe mine or starvation.”
I certainly have no wish to speak for Rand Paul. But speaking on behalf of anarchists, (“neo-” or otherwise), I will say that the traditional anarchist approach to this question is to give people more choices — in particular, not setting up a political apparatus and hope that workers will somehow be able to control it more effectively than corporate lobbyists; but rather organizing grassroots mutual aid networks and fighting, rank-and-file unions that allow mine-workers to effectively stand up to the bosses — so that they do not have to depend on the mercy of the bosses or the solicitude of politically-appointed bureaucrats to gain a safe and humane livelihood for themselves.