No, libertarian can also mean a social conservative who thinks it’s people’s responsibility to govern themselves rather than have the government do it for them. That’s why, for instance, a libertarian might disagree with marijuana use yet support its legalization. To anyone fluent with basic logic, this is not an irresolveable paradox. And there are many other issues that follow along similar lines.
No, there is one thing we know, libertarian DOES NOT mean social conservative.