That’s an excellent question, because I honestly don’t know. I see a lot of hand-wringing and pseudo-philosophical ponderings about “moral principles”, but not a whole lot of arguments based on specific concerns.
It's not that they should never happen, and it's not even protests and boycotts as a whole. It is a matter of principle - specifically reciprocity and infringement on freedoms.
It has a lot to do with the methods being used and the
justification for those methods... and whether or not there are any guardrails that keep the same methods and justifications from being used in other situations.
First, let's look at the infringement of freedoms element.
Consider some of the boycotts when I was a kid, against tuna companies that were catching dolphins in their nets. Some consumers didn't like that, they told the company and other people about it, and they organized a boycott of the product. The boycott is voluntary on the part of other consumers - any consumers who didn't care about dolphins could still buy that product, the people boycotting didn't attack or harass other shoppers. Enough people cared about dolphins that in the end, the company changed how they fished, and consumers were satisfied. The boycott was against the practices of the company as a whole.
Now consider the case brought up earlier about the lead singer of some band who said some nasty stuff. I don't think there's any problem at all with people deciding not to buy that band's songs. That's a pretty standard boycott, and since the singer is an integral element of the band as a company, it's not really something divorceable from the product.
Now, what if instead of boycotting the songs, and refusing the pay for the songs, the people offended boycotted the sellers of the song? Now they're depriving other people of the choice to buy songs from that band. Now they're infringing on other people's agency. That I have a problem with. It would be akin to those dolphin-loving boycotters boycotting all of the grocery stores that carried that brand of tuna, and insisting that the grocers aren't allowed to sell that tuna at all. That also means that other shoppers who don't care about dolphins are being denied their choice of tuna.
That shifts from individuals making a voluntary choice to express their individual perspective on the actions the company responsible... and becomes a group of individuals forcing their perspective onto both other individuals and other companies that are only secondarily related to the problem. It's coercion, not agency.
It's the same principle in situations where an individual person makes an individual statement as a private citizen... and anonymous actors demand their firing from their employer. They aren't acting against the cause of the offense - they're pressuring secondary sources instead. In some cases, the mob extends that pressure to family members as well, even if the family member didn't actually do anything wrong.
I recall a few years ago there was a white nationalist who worked at a restaurant, and gave an interview to someone. People were (unsurprisingly) appalled at his views. People pressured and threatened the owner of the restaurant to fire him. The restaurant owner didn't hold those views, the restaurant owner hadn't done anything wrong. But the owner was threatened with punishment if he didn't take action against the white nationalist. The people appalled at his view also did the same thing with his wife and his brother. There was no information about whether either of them held the same views... but both of their employers were hounded to fire them as well.
Similarly, there was the case more recently of the baker whose daughter had made some pretty nasty anti-semitic comments on line several years in the past. When she told her father about it, he was appalled, and he fired her from her position at his bakery. But that wasn't enough for the angered customers, who threatened his suppliers and his buyers if they continued to do business with him. The owner of the bakery didn't make the remarks, and he had already taken action to fire his daughter.
Those are the kind of over-reach that I find to be unacceptable. Those actions step over the bound of expressing one's displeasure with the source of one's anger, and moves to imposing one's beliefs and will on external parties in order to
maximize extrajudicial punishment for things that are not crimes against the source.
Now let's consider reciprocity.
This takes a little more self-reflection, and consideration for the long-term consequences of the approach.
At heart, complaints against cancel culture are complaints against punishing people for their
beliefs. Several posters in this thread have essentially expressed that people are allowed to belief what they want, but that speaking or communicating those beliefs constitutes an action, and that the action can and should be punished. But that moral judgement isn't something that can be codified in a way that protects against abuse.
The methods that are being supported could just as easily - and just as logically - be turned against you in the future.
I'm going to make an analogy here, and draw a parallel to illustrate this. It's difficult to do, because most of us on ISF share the same core values. I'm trying to find something that will resonate but also be extensible enough to demonstrate the risk.
Back in the 50s, communism was seen as an existential threat to the US way of life. Communism is a belief, a political ideology. Because it was viewed by so many people as a morally unacceptable and dangerous belief, steps were taken to
stop the threat it represented. People were blacklisted, came under surveillance, forced out of jobs, and otherwise mistreated due to their beliefs. Most people nowadays look back at the McCarthy era as a horrible and unconstitutional travesty, and think that we should never have behaved in such a way.
I see the same thing beginning now. I see the same McCarthy-esque persecution when it comes to Trump supporters, to Republicans as a whole, and even to conservatives in general. That was the impetus behind a lot of the reporting and subsequent harassment and persecution of Nick Sandmann. Because he was wearing a MAGA hat, it was assumed that he was an evil person, and thus must be at fault. The reports from the media were highly skewed and painted him as a villain. On the basis of the assumptions about his political beliefs, many people felt that it was completely justifiable to send him (and his family) death threats, and to pressure his school to expel him. Not because he was perceived to have actually committed a crime, or to have engaged in violence, threats or other antisocial behavior... but because he was wearing a MAGA hat. All he did was stand there and smile. But by doing so while wearing a hat with a "bad" political message, he was deemed as a horrible racist person with a "punchable face".
Even after the full story came out, many people - some on ISF - still think that the treatment Sandmann received was justified and acceptable because he was wearing a MAGA hat. Think about that for a moment. Even after having been definitively shown that the initial reporting was false and plain wrong... some people still think he deserved to receive death threats and to be expelled because of his political persuasion.
Now here's the challenging part of this. What if the tables turn? What if, 10 years from now, it's not conservatism that is viewed as evil and unacceptable, but liberalism? What if it is your own political beliefs that are painted as socially unacceptable and justifying retaliatory measures such as Sandmann faced?
Is there any objective reason that would prevent that from happening? Or is it nothing more than your deeply held belief that your views are morally right?
The anti-communists believed that their views were morally right, and that justified their abuse of communists in the US. The anti-trumpers believed (still believe) that their views are morally right, and that justifies the abuse of Nick Sandmann. In the future, there's no guarantee that it will not be the anti-liberals who believe their views are morally right, and that justifies their abuse of
you.
those are the dangers inherent in the principles espoused to rationalize "cancel culture". That it's not
new is irrelevant. It wasn't new when it was witch burnings, it wasn't new when it was the crusades and the inquisition, and it wasn't new when it was McCarthyism.
It's not new, but it is
dangerous.