I disagree.
Say you're the leader of a state. Your economy is based on coal. You have CEO's presiding over various coal companies where their workers are forced to work an average of 12 hours a day, 7 days a week, with little protection from danger or the diseases that come with overexposure to coal. Death is everywhere and malnourishment, dehydration, and suffering are pervasive. CEOs only have to pay their workers a couple of cents. If the workers don't like it, they can always move to another coal company with similar CEOs and similar conditions.
You have two options:
1: Continue the current "free" mode of society, where you, as a fiscal Libertarian, refuse to intervene at all in the economy
or
2: Force CEOs to give their workers protections from danger and disease, raise the wage so that every worker can feed themselves, ban 10+ hour workdays, and ensure that appropriate supplies of water and food are given so that workers don't die. In addition, give workers small, comparitively weak Labor Unions where they can negotiate various terms with the CEOs.
Now, assume that these policies generally help the workers. Answer honestly: is option 1 more "free" than option 2? I say no; to be honest, option 2 is likely more free. But option 2 won't always be more free; if the said leader of the state chose to turn the economy into a Communist dictatorship, we may be as chained, if not more, than we were before. But the point I'm getting at is that it is rare that a removal of power goes on in economics (or, more accurately, rarer than Austrian school types like to think), and thus, compared to our expectations, a removal of freedom is rare. More accurately, it can be said that power and freedom are transferred. In option 1, the CEOs have more freedom and power than others. In the second, the government and the workers have more power and freedom. So I think it's safe to conclude that any free society isn't inherently heirarchical, and any heirarchical society isn't inherently free. Option 1 was more heirarchical and less free, and option 2 was less heirarchical and more free.
As a postscript, I saw you talk about castes and their relationship to heirarchy. I think what you fail to realize is that right-wing politics predate concepts of capitalism and freedom. The term right, as we know it, originates in France, where supporters of the Monarchy sat on the right side of the parliament or whatever. If you know anything about Monarchist pre-revolutionary French society and how it was organized, you know it wasn't very free for anyone in the lower class (which was most of the population). It was definitely heirarchical tho.
Castes, feudalism, fascism, etc. are all concepts that fly in the face of freedom but are, and are recognized as, right-wing due to their heirarchical structure. And heirarchy, along with the preservation of social institutions (these two intersect often) make up right-wing politics. The whole freedom thing was just a rebranding campaign, and it is reflected in the right's views towards gays, abortion, immigration, and trade.
sorry 4 the rant