BHL doesn’t, like most libertarian thought, believe that social justice is a natural by-product of market and non-state relationships which are themselves justified by other values, most notably the freedom of the individual. Instead, BHL believes that such relationships are only worthwhile to the extent to which they actively promote social justice and the well-being of the poor. One leading BHL thinker, Matt Zwolinski, has suggested, for example, that unlike most other libertarians, BHLers would either reject or modify their prioritisation of market and non-state relationships if it could be shown that they do not benefit the poor and most vulnerable.
I take a more straightforwardly consequentialist view. If I discovered that the libertarian institutions I wanted (a “night watchman” state, perhaps with a modest safety net, although I doubt that would be necessary) were not the best way of allowing people to satisfy their preferences, I’d want whatever institutions did do that. That’s all any political ideology should offer – the best means to allowing people to do whatever they want to do.
The article is a little bit off-base when it contrasts Bleeding Heart Libertarians with common or garden libertarians:
They share the libertarian suspicion of the big state on economic issues and are critical of high tax, interventionist policies, ‘crony capitalism’ and the loose money policies of the Federal Reserve.
However, unlike some of the loudest elements in the Tea Party (or indeed in UKIP) who might share these economic views, they are also supportive of civil liberties in the form of gay rights, anti-racism, internet freedom, legalising marijuana use, feminism and more open immigration.
They are also highly critical of American foreign policy opposing the ‘war on terror’, military action against Iran and other forms of intervention. (Although it must be reiterated here that BHL remains a dialogue of diverse views rather than a manifesto to which all sign up.)
Most of those things seem like pretty integral parts of the standard libertarian agenda to me, not the wacky innovations of the Bleeding Hearts. I’d certainly do a double take if I met a libertarian who was against liberalizing drug and immigration laws, but enthusiastic about more foreign intervention. (I don’t necessarily blame the RSA’s author for this, mind you – the number of old-fashioned conservatives who call themselves libertarians without any support for free people or, indeed, free markets is truly depressing.)
What sets the Bleeding Hearts apart from normal libertarians is their belief that social justice of the kind outlined by John Rawls is an important value which libertarian institutions are good at achieving. Matt Zwolinski briefly outlined this argument in this video.  (Jacob Levy disagrees about the importance of social justice  — some of the reasons he gives are why I prefer old-fashioned 'utility' to 'social justice'.)
In any case, it’s good to see more mainstream interest in libertarianism, particularly when it’s fair minded. With the right degree of open-mindedness, optimism, and confidence in the power of liberty to improve people’s lives, libertarians might have a uniquely appealing idea on their hands.