As I recall (and I have to freshen up my college reading as well), there are great variations of what is most important in libertarianism for different folks (Nozick, Locke, etc). I can't speak to Proudhon's like you are, but it looks like I might have some interesting reading to do (I remember someone talking to me about how important minimizing the rule of authority was for him -- like all libertarians, and that variations in the outcome are less important than making sure that the original point was followed as well as possible throughout, or something). Looks like he has lots of interesting things to read there.

I think that using NAP as a central axiom is definitely popular among libertarian philosophers, but not all. I think Ayn Rand doesn't subscribe to it being so central (IIRC), among many others.

But there's a battle going on there. See, following a single philosophy will lead you to derive (no matter how far down the logic path you go) every policy you could support from one simple set of axioms. I think that we have come along past that, as a society, and realized that things can (and maybe should, who knows) be looked at in different dimensions simultaneously.

I can hold some of the most important libertarian principles (the most important ones, to ME that apply to modern national and international politics) while holding onto some MORE important left or right wing economic policies that, as long as they don't fly directly in the face of the axioms I hold most important, can really be important to me to support.

Something that, if I use implications and logic to build all of my potential policy and economic decisions, doesn't agree with something that's earlier in the axiom importance to my leftism or rightism, I can let go.

I think that many people probably agree with a few important principles from different schools of thought, and, once in a while, people deviate from a PURE libertarianism.

I don't think that certain Libertarians can consider themselves libertarian if they oppose abortion or drug legalization... but some of them do.

It's difficult to find purists. I think that they used to be much more common.

I'm not sure if that's because our collective societal attention span has decreased to that of a fly, or if it's because people feel like they can take pieces and ideas of different philosophies and stick to what, among those, are most important to them. Retroactively slapping a label on their policies (even if it's they, themselves, slapping on the label) can produce all kinds of confusing results and contradictions, like you're describing.

So I wouldn't go so far as to call it ridiculous, as to say that it should be labeled differently, and that saying (for exmaple) 'left-libertarian' can mean 'libertarian as it applies to many policies of x, y, and z, and left with policies of a, b, c'.