It would take a massive Venn diagram to illustrate the overlaps between libertarianism, marxism, anarchism and even statism (minarchism has a small component of statism, marxism a huge component prior to the never-occurring "withering; anarchism has none.).
Frex, we agorists (who fall under both the libertarian and anarchism Venn circles) believe there's a lot to be said for marxist class theory. His biggest failures were the misidentification of the ruling class, which we recognize are actually the politically-connected, and his desperate clinging to the already-discredited labor theory of value, which made all his economic analysis indigestible.
In that Venn diagram, anarchism is a big tent. You'll find many, many anarchists in support of civil liberties, and an entire wing of anarchistic thought that encompasses free markets, in direct opposition to the crony capitolist system we have today that often (
intentionally and maliciously, imo) gets conflated with free markets.
In both cases, the argument is that the biggest violator of civil liberties and free markets is the state, not the individual.
Look around you at today's societies and it's not hard at all to see the validity of that argument.
Minarchists believe it's necessary to have a state to protect civil liberties and free markets, and in all other areas stand down. There are minarchists that argue that the Constitution was essentially a minarchist document. A simple review of the growth of the state in the US shows that minarchism devolves over time into foxes guarding the henhouse. Lysander Spooner noticed that over 150 years ago.
Lysander Spooner said:
But whether the Constitution really be one thing, or another, this much is certain - that it has either authorized such a government as we have had, or has been powerless to prevent it. In either case, it is unfit to exist.
ETA: And calling Ayn Rand the central theologian of libertarianism is laughable. She has been quoted time and time again as considering libertarians nothing more than libertines. Ayn Rand also believed in interventionism. She's more a poster child for conservative interventionist minarchism than a libertarian.