It's hard to get enthused or worked up about political shouting matches over purveyors of fried chicken, but I think the recent kerfuffle over Chik-fil-A could prove illustrative in the right context. For those out of the loop, Chik-fil-A is getting hammered by sexual-equality groups for some anti-gay-marriage statements made by one of its proprietors a couple of weeks ago. Of course, the general views of the very Christian owner(s) of Chik-fil-A have been known for quite a while (anyone wonder why their doors are closed every Sunday?). But social media outlets seem to be useful for putting old (and often, even untrue) stories under a magnifying glass. And the views are indeed sometimes quite myopic...
I won't pick apart the disparaging claims bandied about by "conservatives" or "liberals" on the subject. That would be a bit pedantic at this point. What I think is interesting is that the libertarian response (at least among my small circle of that world) is pretty varied. I actually find that kind of comforting in a weird way. A lot of people tend to think of libertarians as a very narrow and homogeneous group. And, indeed, as libertarians are generally sticklers for consistency, you might think we'd have a very clear prescription for such an issue. I think some people may have even at one point called us "cultish" for such things. But it's actually a somewhat complex issue upon reflection. And the variance on this subject among libertarians actually highlights a very real diversity among us.
With that in mind, here's how I see it...
It's not an issue of justice. Or at least, if it is, there's a whole lot of fuzziness. Chik-fil-A does not turn the machinery of the state. They may give money to people who try to talk to people who turn that machinery, but they're not turning it. So, from a thin libertarian perspective, that's going to be an important part of this equation. If this kind of consideration grounds your concern, we could expect a somewhat neutral view on suggested boycotts.
However, under both a thin and thick conception of libertarianism you could make a good argument for supporting the boycotts. On the thin end there's certainly a good argument for withholding your business from people who support (even if not directly) things you find unjust. And it's certainly well within your own rights to do so. On the thicker end there are good arguments for believing that a society that does not support sexual equality would also not, adequately, support a framework of institutions that are more libertarian-friendly.
There's also a (somewhat) thick argument about the limits of "support" perhaps. If you're supplying arms to the Third Reich there's an argument, on thin grounds, that you're not directly killing people so therefore there is no true injustice. But it's easy to see how one might oppose, in a very libertarian fashion and for very libertarian reasons, such things.
But what I'm kind of interested in is a third level of critique (not sure whether to call it thick or thin) that questions the limits of such conceptions. For one thing, I think appeals to tolerance could be ushered on both sides of the argument. Surely there are arguments that a libertarian society would be more workable or coherent when tolerance is embraced by all; but that might also lead you to believe that if we want to foster an appreciation for freedom, or more importantly discussion, in those we disagree with, then we might be well-off to show a certain degree of tolerance for them as well.
That doesn't mean that we have to agree with them, or do business with them. But I'm not sure that threatening to practically excommunicate all whom we disagree with is particularly libertarian either. I want those people to be public with their opinions, and even vociferously so. It's a point of engagement. I want fear and hatred to be curtailed and defeated. I don't want it to be simply swept under a rug to be perpetually bandied about in indirect ways for generations.
However, even if we believed market-based excommunication to be perfectly libertarian (and there's certainly good arguments for it) I'm not sure how much sense it makes on a practical level. Let's think about this. We're saying that we should actively abstain from doing business with actors that give money to people who push for political change that we find to be unjust. If we were being consistent, wouldn't it apply in the other direction as well? Maybe you own a small or mid-size company in Nowhere, USA. You're picking up employees left and right to keep up with increased business. Now, to a libertarian, there may be no injustice in screening potential employees on the basis of their political views. But would it be a practical or wise thing to do for libertarianism in the long run?
Granted, it's probably relatively easier for consumers do this. But it's not clear why it would be less of an imperative (politically) for employers. I mean I can't give money to someone with an Obama sticker on their car, right? There's a good chance that they are taking some of that money and contributing it directly (or indirectly) to his campaign. And I don't think the idea of blowing up innocent Pakistani children with drones is particularly libertarian. So, if we're going to be consistent, I guess we could say that I should only hire people that support my views, right?
You can see how this could get kind of sticky in a hurry. On a related note, this is part of why I've found the state-based conception of "discrimination" (or rather its prohibition) nonsensical. In their case, the consideration is flipped. Employers aren't "allowed" to discriminate based on any number of things generally perceived to be outside of the realm of meritocratic considerations. Yet, for whatever reason, it's perfectly fine for customers to engage in such discrimination - which might even be more detrimental/appalling on the grounds of severing bridges to wealth accumulation. In a legal context, it's perfectly OK for people to decide to never do business with a company because it's owner is black, Hispanic, gay, etc. It's not clear to me why this is acceptable when the other is not...but this is a tangential conversation.
My broader point isn't to say that there is any particular "libertarian" view in all of this that is "right", or that should prevail in any meaningful sense. I just think it's interesting how nuanced the opinions can be in a framework that is thought to be pretty restrictive. I get the impression that most people think we drank the Nozickian KoolAid at some point and just punched out. But, at least from what I read, it turns out we're not all mind-numbed robots after all. Well, the others are maybe. But not me. I'm cool like that.