I envision something being spun from some aspects of libertarian philosophy and some nature of coalition with those who identify as "Libertarian" to avoid the persecution of true Catholics which I foresee being on the near horizon. I simply and bluntly refer to that primary aspect that I can see us needing to spin to our advantage as "leave us the hell alone."
I gave the libertarian party a shot inasmuch as, out of disgust with the dominant parties, I took the time to evaluate each of their 2016 presidential candidates listed on the party website. What I found was a mixture of dumbasses, abortionists, and, most astounding for that party, a few neo-cons. The libertarian party as currently configured is a no-go for me. But I could see another third-party stealing away some libertarian members, or, perhaps, the right people getting involved in the party and working to change some of what's wrong with it.
I see that the "leave us the hell alone" fiber that is Libertarianism would not be good if something such as a good Catholic monarchy had a shot at coming to power. But since that is simply daydreaming for now, we as Catholics can achieve something of a short-term reprieve from govt oppression through a strong "leave us the hell alone" movement. Without such a reprieve, govt is going to require every hospital offer abortions, every medical student (and some others in the medical field) participate in abortion, outlaw homeschooling, force holohoax be taught ad nauseum, employers provide abortion and contraceptive insurance coverage, etc., etc., etc.
I see what can be taken from, or exploited from within libertarianism, is protecting Catholics and Catholic institutions from such govt oppression, simply long enough to avoid/mitigate the storm--maybe, optimistically, give us a generation or two of a breather to grow our children and gain some converts, and hopefully see the Chuch regain its proper power.
As far as the example of faggotry, I think the Democraps are much worse than libertarians. You won't find a true libertarian who'll make you bake a cake for a faggot wedding. But you can be sure that Obama, Billary, Sanders, and a high percentage of Dems in congress would make you do so.