Public witch hunts are called "witch hunts" for a reason, and it's not a pretty one. It's also known as "mob justice", which despite the name is generally considered to be not justice at all.
It seems poorly considered to characterize social pressure as a witch hunt. It is acceptable to encourage others to share your moral convictions, there is a vast gulf between that and a pitchfork mob.
I definitely would, since the response to Shkreli has been primarily online ranting. He's never been at significant risk for physical harm as a result of the public discourse as far as I can see. I don't consider negative public opinion and castigation for unethical behaviour to be unwarranted or undesirable, so I can't see that rising to the level of vigilantism either.
In my view, society would become severely dysfunctional if we are expected to withhold our negative views of someone's choices, from fear that too many people will share those views.
Public witch hunts are called "witch hunts" for a reason, and it's not a pretty one. It's also known as "mob justice", which despite the name is generally considered to be not justice at all.