You can be a libertarian and a PRL since they’re theories that answer different questions. Libertarianism answers the question, “What institutional structures are good and just?” PRL answers the question, “How do we live on moral, peaceful terms with people who disagree with us about which institutions structures are good and just?”
Sometimes PRL and libertarianism conflict because libertarians often say they want to pursue establishing libertarianism without concern for non-libertarians who object. But in practice, libertarianism and PRL rarely conflict….
Via Libertarianism & Public Reason @ Bleeding Heart Libertarians.