The boycotting itself isn't the problem. The problem is boycotting anything and everything that could be considered outside the narrow view of what's "acceptable"
Why? Those same dollars will still be spent purchasing an alternative to what's being boycotted.
I understand that this
ends badly because it's an oscillating effort that eventually causes a destabilization. But that's a function of all systems with individual actors. Unless 'they' stop doing it first, it's necessarily part of the the toolkit.
Hell, huge swaths of institutional racism was done through the boycott. "I won't hire blacks" is similar to a boycott and eventually required legislation to address, and the legislation was required because moral suasion to end the boycott was insufficient. But just because it ends badly doesn't mean that people can stop doing it.
If some information is deemed to be socially necessary and is insufficiently provided by voluntary funding, the backstop is government funding. We use it all the time.
Even if there would be aggregate benefit to 'both sides' doing it less, there's no individual motivation to subsidize something you think is harmful.
Edit: and the entire game-theory is confounded if someone is making a 'reasonable appeal' to people they disagree with to
boycott less. Everyone within fallout range of nuclear targets understand the value of de-escalation and disarmament, but those are negotiations between governments with verifiable conditions. But, at the level the game is played, getting your 'opponents' to 'try less hard' is the same as getting your own side to
try harder, because it's the results that matter.