Many (not all, maybe not even most, but definitely a good amount) libertarians are environmentalist and see the EPA as a valuable tool to ensure that people's rights are violated.
However, in general the cause is the same but the approach is different. For example, just of those two causes should be handled by the courts (as a libertarian sees it at least) rather than through regulatory agencies.
To rephrase, Libertarian's generally agree people should be safe at work. They just disagree with the top down approach to solving that issue.
In certain narrow situations where there is an identifiable property right at issue (e.g. dumping waste on private land). But there aren't a lot of libertarian theorists espousing a general "right" to untouched wilderness, preserving endangered species, or having clean rivers.
> To rephrase, Libertarian's generally agree people should be safe at work.
Libertarians generally believe that the level of safety in the workplace should be set by the market, rather than by a regulatory agency. I.e. if a workplace is known for being unsafe, it won't be able to hire employees (or will have to pay a premium for employees to take on the extra risk). Liberals in contrast believe that the government should impose a safety floor on all workplaces, irrespective of the market.
To me, this is where the libertarian philosophy loses its internal consistency. For two reasons:
1) There is no such thing as a closed system, so land use is fundamentally social
2) For the most part, all existing property deeds were obtained by force, not through the voluntary agreeing to contracts, so no one who holds a deed really has any kind of moral claim on it.
Libertarians have to fall back on some other political system (manifest destiny, kraterocracy, democrasy, etc) to resolve the land use question. But to me land use is the foundation of all property law and the fact that Libertarianism has nothing to say about it makes it largely useless as a foundational political system. It's a nice thing to think about, but it can't be relied on to answer basic questions.
Essentially this highlights the difference between your particular policy opinions and your enthusiasm for having a government enforce those policies on everyone.
On the other hand, in my experience, libertarians are pretty far from being liberals, and even farther from being typical Democrats. Personally, I share even less with typical Democrats than with typical (non-Trump and non-Evangelical) Republicans. I do share a lot of social beliefs with people who consider themselves to be liberals first and foremost, and agree with them about some of this nation's greatest challenges. I've found typical Democrats to be against drug legalization and only with great hesitation have started supporting LGBT rights, when most libertarians were supporting gay rights 40 years ago (in the sense that gays rights mean that gays have the same rights as everyone else, because what people do in the privacy of their homes is not the government's business).
Anyway, I think it's fair to say that there's support for BI from two different parts, if not sides, of the political spectrum.
But fair point about there being left libertarians and right libertarians, I don't really disagree. I mean, Chomsky calls himself a libertarian, but is definitely "of the left" (and I happen to disagree with him on a lot of issues, yet share some of his core beliefs about the dangers of government and authoritarianism). I'll take more care in the future.
To be fair I think "The Libertarian Left" would also be miss-leading. We defy the left and right labels :)
By world standards, not to mention many past US standards, the two presidential candidates (and the current president) are clearly right-wingers.
Many (all?) libertarians lean left on a great many social issue and consider the social part of libertarianism as important if not more important than the right leaning economic part. I think the term "libertarian right" while not an incorrect term at face value -- there are in fact right leaning Libertarians just as some Democrats are further left than others -- is miss-leading and can potential lead to misconceptions about Libertarians as similar to Republicans. I for one share much more in common with the Democrats but I am very definitely a Libertarian.
I think many of us would prefer you just use the term Libertarian and leave off left or right.
Edit: or perhaps if you were in-deed referring to the conservative party, add some clarity and say "Republicans that lean Libertarian"