On a political spectrum, the term libertarian should relate to anti-authoritarian. So, I can see how the case can be made against socialized healthcare for them. It's not really about true freedom or liberty. And in the US anyway, it's largely just facade co-opted by the fascist [authoritarian and wealthy] right wing, ironically.
The word "Libertarian" in US has less relation to the dictionary definition than "Republican" and "Democrat". These are names of parties over here, even if they have a namesake of governmental mechanisms.
Examples:
Ron Johnson said in a single breath that he was a libertarian and opposed the legalization of marijuana.
Find the average "libertarian" policy position on border policies.
US politics is unfortunately entrenched in tribalism rather than searching for the right tool to match a job or solve a problem and maximize outcomes, the libertarians over here are no exception.