There is no libertarianism without an underlying foundation of egalitarianism. Rhetoric that tries to portray egalitarianism as the inherent polar opposite of libertarianism isn't just bad, toxic messaging; it's wrong as a matter of theory. Anti-egalitarian libertarianism is an incoherent contradiction in terms.
Private property, self-ownership, non-aggression... or whatever other variation or combination you prefer. None of it works without a basic starting point that such things apply reciprocally and universally, and thus equally, to all persons.
This isn't exactly rocket science or a difficult concept to grasp. We all know the famous words saying the same basic thing in the Declaration of Independence, and thousands of other places. The leap from fundamental human equality to universal individual rights is political philosophy 101; not just for libertarianism but for the entire broader tradition of Western liberalism.
Anything else is just bickering about which group gets what privileges-- not "rights"-- and who gets to decide that hierarchy. It's a bunch of rationalizing and excuse-making for why certain collective groups should be granted more privileges than others. It's closer to Marxist class theory.... or, more often, straight-up racism... than anything resembling individual liberty.
Anti-egalitarianism is a doctrine that is authoritarian to its core, the very seed from which authoritarianism grows. That's true no matter how much sophistic anti-government window dressing you put on it. If rights and freedoms don't apply to everyone, period, then all you're doing is setting yourself up as the authority to decide who does or doesn't get them. And it rapidly becomes depressingly predictable what sort of prejudices and baser impulses drive that process.