Ryan and Rand are certainly interesting figures. Like many people, they have some things in common, and other things not in common. For example, one of the things they have in common is that…neither of them are libertarians.
Ryan identifies as a conservative, and while many libertarians idolize Rand, she did not want her movement of objectivism to be confused with libertarianism, and as best as I can tell she despised every prominent figure of 20th century libertarianism.
Commonweal - dotCommonweal
Libertarians and libertarianism have been receiving a lot of attention lately. In the current issue of Commonweal, Eduardo Peñalver asks whether Catholics can be libertarians. His answer: It depends—not on what kind of Catholic they are but on what kind of libertarian:
For Ayn Rand and others in the natural-rights tradition, property rights are conceived as virtually absolute in scope, limited only as necessary for the protection of other property rights. For these libertarians, the protection of property rights—the freedom from interference by government—is a moral imperative, irrespective of the outcomes it produces. In contrast, for libertarians whose outlook is based in economics (think Milton Friedman), the commitment to state noninterference in private-property rights rests on empirical—and, at least in theory, testable—claims about how the world works. Maintaining robust private property rights is good, the argument goes, because it leads to the more efficient operation of the economy, which in turn generates greater overall social wealth from which everyone benefits.
In my view, the Ayn Rand, natural-rights libertarianism that Paul Ryan has flirted with is fundamentally incompatible with Catholic teachings on the nature and limits of private ownership.