I'm not sure that an arch-libertarian would be committed to the view that a mob influencing actors in a marketplace is best understood as the invisible hand working things out,
The whole point is that it's not some mob pushing poor companies into doing what they don't want, but the companies themselves deciding what best suits their bottom line. No mob can just walk into the quarters and fire someone. Someone up the company totem pole has to decide whether they want the negative publicity.
Like, do we want to keep Steve, who thought it would be smart to start the shareholder meeting with a fecal joke about the Islam, or do we want to keep doing a lot of business in the middle east. (Which, again, actually happened way back.) If it's the latter, sorry, Steve, you can pick up your things and don't forget to hand over the RFID card and company car keys at the reception.
All the mob can do is basically
1. pass the information around. Which, as I'll remind you is actually part of the free market theory. It really involves perfectly informed everyone.
and
2. vote with its wallet. And, again, basing your choices on that perfect information is also a part of the free market theory. Plus, isn't that what the right-wingers preach that should be the case, as opposed to government regulation?
But again, it's up to the company to decide whether said wallet is worth it.
Of course that won't stop idiots from arguing that, oh noes, black is white, up is down, north is south, and business decisions are anything but just that, if it's against the kind of bigotry they like.
Or more to the point that, that you
1. don't have a right to free speech, if it cancels theirs. As in, they can spew bigotted crap about you, you're some monster if you even comment on them. And
2. that some company has some weird right to your cash, whether you like them or not. Which isn't even left or right wing, it's just stonking stupid and entitled. Look, we're not against anyone earning money if they can, but the notion that someone must keep giving any particular entity their business, no matter what that entity does, is just plain old entitled.
Well, or at least that would be the implications, if they thought it through. Most often they didn't. They just think that they have some right to be bigots about everyone else, everyone else doesn't have a right to even comment about THEM, and something's wrong with, well, everything, if it doesn't work towards that state of affairs.