Honestly, I don't get how "Constitutional Republicanism" is really supposed to be compatible with Libertarianism. In fact, I kinda the two ideas to be pretty incompatible with each other. Let's take abortion: plenty of libertarians play that "states right" card when it gets brought up, including Ron Paul until recently. What does that even mean-- people are entitled to certain liberties and the bigger scale, but your local government is authorized to tyrannize you however they want, granted there's no Constitutional precedent on the issue? Likewise, I saw Rick Perry get rebuked in last weeks debate for letting immigrants working towards citizenship drive their cars.
"Liberty" means "liberty for everyone," not just "liberty for members of the state." Ultimately, ideas about state and even national boundaries are outdated according to the libertarian view, but for very obvious reasons they can't be completely done away with-- especially when the most influential libertarians these days seem to be heavily tied with the US political establishment. The end result is a pretty weird way of approaching certain issues, like the contradictions I noted above and the ones in the OP.
Is the solution offered by US libertarians better than the current establishment? Certainly yes, at least in some ways. But it also can be worse, sometimes. I've been thinking about the question a bit since the topic was posted and, I've got to say, I'm started to see what the author was talking about.