The author of the linked page didn’t go into a lot of detail about his overall libertarian philosophy, as he was preoccupied explaining his Calvinism. Mainly he said he opposed prescriptive and restrictive laws like those against illicit drugs, hate speech, gun ownership, etc.
There is nothing intrinsically contrary to Catholicism in such a philosophy. However, like any political philosophy it can lead to negative effects, and it is incumbent on Catholics to consider what they can do to minimize these effects. So for instance if meth and crack are legal, are there ways that their use can be discouraged by families and private institutions, and addicts rehabilitated?
In addition to what the linked page described, usually libertarianism is opposed to the appropriation of private assets for the common good. Perhaps the reformed libertarianism omits this plank of the philosophy?
On this topic, you will find many writings of popes and prominent Catholic philosophers who suggest a role for government in providing for the poor and those who are most disadvantaged. However, I don’t think Catholicism truly requires governments to levy taxes or seize property in order to achieve this end. If private individuals and institutions are able to do this job, the government need not involve itself.
In the real world, most libertarians are not purists. They may accept the need for a small level of taxation to support the armed forces and police, or accept government creation and maintenance of roads, or regulation of utilities. So usually the ideals described are goalposts, and libertarians favor moving the ball in that direction from the current status, even if they wouldn’t establish a purely libertarian society if given the chance.
