[…] Or are there…
. . . Or are there aspects of a genuinely free market which Carson, Konkin, Rothbard, and other market anarchists would reject as unacceptable – though uncoerced?
Speaking only for myself, provided that “reject as unacceptable” means nothing more than “consider subject to moral criticism and deserving of nonviolent protest,” I’d say sure, of course there may be aspects of a genuinely free market which turn out to be something that libertarians ought to reject as unacceptable. Systematically uncoerced exchange guarantees only that transactions will be free from injustice. But while justice is a virtue, it’s not the only virtue, and if the people in a given culture tend to have despicable values they are willing to pay for (say, white supremacism, or misogyny, or irrationalism) then there will tend to emerge despicable markets that freely serve that demand (say, a market in minstrel-show iconography, or — I think — the modern pornography market, or markets in various sorts of flim-flams such as astrology or spiritualism).
That these transactions would be uncoerced does very little to defend them. It does establish that the nature of the problem has to be identified in terms other than the terms of injustice, and it also establishes that the means of trying to change the situation must not involve the use of force (e.g. boycotts, strikes, moral agitation, etc.). It may be that these sorts of protest are called for simply on their own merits — because besides being a libertarian, you also happen to be an anti-racist or feminist or whatever. But I think that in these specific cases (and in many others) there are also deeper connections between libertarianism and specific cultural and philosophical positions. It’s not that libertarianism entails them (both misogyny and feminism can exist within the boundaries of the non-aggression principle), but rather that there are various sorts of logical and causal connections between the values entailed by the positions, and the grounds for the positions (as I discussed in New York last year).
Does this clarify, or muddify?