You clearly don't understand Libertarianism. This is yet more evidence.
We have different understandings of Libertarianism. Which one is more accurate I believe is up for debate. Or, maybe more accurate, which understanding is more useful is up for debate. My sense is your much more focused on the spherical cow definition of libertarianism, while I'm much more concerned with how libertarian plays out in practice as, well, a practical ideology. Then again, all models are going to be somewhat abstracted, so it comes down to, well, who's abstraction is more useful. A point we obviously disagree with.
See this concept of common good? "Desired lifestyle"? None of those are libertarian things. Now you can design a philosophy around such a thing, but that philosophy is not libertarianism. The idea of limiting a persons freedom for some kind of common good almost certainly violates the NAP, for example.
But the above are all necessary cores for a practical philosophy. And Libertarians cry they do have them with the declaration that Libertarians are not anarchists and believe in the need for some coercive state. And thus their belief in "the idea of limiting a person's freedom for some kind of common good".
Practically, both in how libertarians define themselves, and in many of their arguments (freedom here will increase public good is a common libertarian argument for things), Libertarians implicitly adopt the idea of a common good. Some common good exists that needs a public entity (a state or similar such organization) to manage that unprivitizable commons. Freedom will lead to good outcomes, which means there are other goods besides freedom, which the necessity of the state suggests these other goods can be weighed against freedom, and less freedom can be more benifitical than more.
And later, you somewhat recognize this by saying that Christian libertarians want a Christian society which they find as a common good. That's the Christian in them, not the libertarian. Also, on top of this, Christian libertarians won't limit freedom to achieve a common good in violation of the NAP, or they quite simply aren't libertarians. Which is of course why Marxist libertarians either aren't Marxists, or aren't libertarians.
Once you recognize the public good, or even some idea of good things besides freedom, recognized by the need for collective action through the state or other options, you need an ideology that deals with that common good and other goods.
Even below ideological completeness, on simple practical organization you need to be able to point your people to some common vision to push for. I agree Libertarianism in its pure form doesn't have that, which puts them in the same problem the post-modernists had where declaring there are no meta narratives doesn't give you anywhere to go. So, despite them theoretically being opposites, the post-modernists after declaring no meta narratives then need to sneak Marxist meta narratives, because without it all you can do is how many angels on a pin navel gazing. And thus the non-Marxist postmodernists have mostly seemed to become irrelevant.
I believe Libertarian has the same issue: its missing so many core needs for a functional ideology, such as adding clarity to what that common good is and what freedom working looks like, that it inevitably needs to be mixed with some other ideology to be something whole and functional.
Once you recognize a common, you need some theory of how that common should be managed. Should the common be managed at the lowest practical level, with the goal of maximum subsidiarity? Localist Libertarians. Or is it better to have as big a ruler as possible, to maximize uniform and fair rules, a globalist Libertarianism, like Yaron Brooks seems to argue for in some of his pro-EU discussions?
That is just one issue that, practically, needs some resolution, and by very specifically trying to be agnostic on the question of what the common good is and how they should be governed, Libertarianism doesn't directly provide much in the way of answers. Thus, some other ideology becomes necessary to fill in those gaps, and often that other ideology is adopted unconsciously, creating denial and unself awareness of what is actually being argued for. You've heard this argument before in the "libertarians handmaid for socialism" thread, where I argued many libertarians practically have bought into a lot of socialist beliefs on what the common good looks like, mostly unconsciously, which leads them to pushing for socialist ends, even though the believe they can get there through non-coercive means. However, since Libertarian very explicitly states there are necessary exceptions to the non-coercion principle, those beliefs in socialist ends will inform their beliefs of where those reasonable exceptions will be, in a pro socialist direction.
And, to be clear, I am using Socialist to refer to the whole socialist/Communist/Rousseauian/Hegelian school of thought. Just to avoid confusion over thinking I'm referring to very narrow school of thought.
The Distributist? Not a Libertarian as far as I can tell. So his opinion? Entirely orthogonal to what libertarianism is as a moral/political philosophy. Now he might side with libertarians on many issues because we agree on stuff, but that doesn't make him a libertarian.
I'm not sure what point your making here: of course the Distributist isn't a libertarian: in his formal videos, proably a 1/3 to a 1/2 of them are specifically about refuting liberal/libertarian ideas, and he sees Libertarians as one of the major things holding the right back and letting socialists win.
My main point with bringing him up was that people in a debate he was in couldn't really wrap their head around the idea of freedom/democracy explicitly not being the primary, goal of a persons ideology.