In modern (western) political discourse, we've formed a sort of dichotomy between things like liberty vs equality, or big vs small government, or private vs public. The prevailing view is this: there is a scale between the two elements. The left tends to favour a larger state, equality over economic freedom, and the public sector over the private sector. The right, on the other hand, tends to favour smaller government, economic liberty and the private sector over the public one. At least in the context of liberal democracy, then, every action (more or less) that adds to the size of government is left wing whilst every action that takes away from it is right wing.
Of course, left libertarians of all stripes are left out of this model. We want less government and more equality, and view these two positions as mutually reinforcing rather than moderating. A lot of the disagreement between different sorts of market libertarians comes from different analyses of the role of the state. Right libertarians view capitalism and the state as two essentially conflicting elements. Less government, to them, means some vague conception of more "pure" capitalism. And capitalism, of course, is the condition of liberty.
Left libertarians disagree. We see capitalism and government as two sides of the same coin; elements which strengthen and perpetuate one another. We're skeptical of libertarianism's modern alliance with the right, which has become in some ways far more "statist" over time. It's also fallen prey to this dichotomy between small and big government, an influence of conservatism, which leads it to some pretty detestable positions. This is my beef:
Government intervention doesn't build itself up in such a linear fashion. The government doing a thing doesn't necessarily place you one step to the left or right, especially in the structure of liberal democracy, with its scatterbrained policy makers. Instead, we see a patchwork of intervention, intersecting and contradicting itself at every turn. Individual interventions are reactions to existing interventions, and often exist to ameliorate negative effects. Thus, the libertarian should not oppose all intervention lest we end up with a more authoritarian structure overall, but rather specifically attack root cause interventions, or primary interventions.
For instance, I don't believe that a consistent libertarian should oppose the existence of the minimum wage without taking into account the context surrounding it. Now, obviously, in a perfectly libertarian world (whatever that is), the minimum wage must not exist. However, we don't live in such a world, and our current economy is filled with distortions and privelages which actively depress wages. The regulatory state creates artificial barriers to self employment and sustenance outside of the hierarchical firm (which would increase bargaining power), and decreases competition for labour. Thus, the value of labour is depressed and the minimum wage becomes necessary. To remove this distortion whilst refusing to attack or acknowledge the factors it seeks to ameliorate, you end up strengthening structures of authority.
In other words, our current system, including the minimum wage, is like breaking someone's legs and then paying their medical bill. The liberal says "we should pay more", the conservative says "we shouldn't have to pay" and the (consistent) libertarian says "we shouldn't have broken their legs in the first place".
Even the side of libertarianism that has been poisoned by the right will occasionally build on this sort of structure. For instance, if you happen upon a libertarian who opposes immigration, you can pretty easily guess what their argument is, and probably that they got it from Milton Friedman. They'll say that in a genuinely free market, they'd oppose any state restrictions on this sort of thing (an exchange between people from two different countries is still a voluntary exchange, and the state has no place stopping it), but, since the welfare state persists, they're forced to support it because (obviously) the lazy immigrants will come and leach off of their tax dollars. Thus, we need strict borders until such time as the welfare state dies.
It's exactly the same sort of analysis. It says that, in a genuinely free market, a specific distortion would not be necessary, but since we live in a very unfree market, that distortion is necessary to ameliorate another distortion. However, the right libertarian would do well to dig a little deeper and look at elements which the welfare state exists to ameliorate in the first place before they oppose immigration. The regulatory state has, historically, destroyed voluntary, mutual aid based bottom-up social safety nets. Things like friendly societies, mutual organizations, church groups, organizations for pooling costs and so forth have been actively destroyed by the state. In other words, the welfare state is necessary because our ability to provide one ourselves is squashed by government.
I think when libertarians apply this sort of analysis so selectively, it's pretty revealing of their ultimate motivations. When the interventions that destroy the power of average people aren't recognized, it's easy to dismiss interventions which ameliorate those effects. It becomes corporate apologia and wealth fetishism. It contributes to this view that liberty is just Walmart minus the state, and that billionaires and suits are the ultimate casualties of authority. We should acknowledge that liberal reforms like the welfare state and minimum wage are, ultimately, bandages that don't get to the root of inequality or structural poverty, but you cannot oppose those solutions on those grounds alone without first looking at their raison d'être.