I think it would be a helpful to discuss whether libertarianism should even be considered a branch of conservatism. Say what you will about the high-minded goals of libertarianism, but my observation of most living breathing self-identified libertarians on this board leads me to conclude that many are souless amoral narcissists who want government out of their faces so they won't have to pay taxes, can indulge in their pot habit, and consort with prostitutes without fear of government interference. Most I've seen here have no sense of civil responsibility, and are down on the concept of civic virtue. They're impractical and selfish, and, frankly, I'm tired of hearing them each election cycle threatening to boycott the Republican candidate. They should make good on their threat and take a hike. We'll muddle through without them.
The vast majority of screamers here on FR believe that libertarians are a bunch of pot heads, but the truth is that most libertarians don't give a rat's behind about drugs. They want what Reagan was offering, smaller, less obtrusive government. If we throw them out of the tent, the tent is going to get a lot smaller.
You are still confusing libertarians and Libertarians. They are completely different.