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Boycotting animal products is quite effective on its own. Avoiding eating one single egg prevents around 24 hours of chicken suffering in expectation, which is pretty significant. Eating one more chicken causes around 30 days of additional intense chicken suffering. Your boycott would have a very significant impact in expectation.
The problem with animal product boycotts is that we haven't discovered a robustly cost-effective way of getting other people adopt a plant-based diet. My current position on this issue is that: "It's impactful to go plant-based, but it's very hard to get other people go plant-based".
This is just a quick answer to point out that veganism (which you mention in the question) is a bit different to other kinds of boycotts.
In a conventional boycott, you refuse to purchase certain kinds of products until the organisation(s) who sell them change their ways. I don't know much about how effective those kind of boycotts tend to be (although I think there are some famous examples of where large scale well organised boycotts seem to have produced some powerful results, e.g. montgomery bus boycott).
But veganism isn't just about pressuring organisations to make some policy change. You don't need large numbers of people taking part in order to have an impact. Each individual vegan who stops buying animal products will lower demand for animal products, and therefore reduce the number of animals who are raised for food (in expectation). It's not a binary "stop factory farming" or bust. Every extra vegan reduces the number of animals being raised on farms (in expectation).
Could the same logic be applied elsewhere?
E.g. boycotting Nestle results in reduced money for Nestle which causes Nestle to exploit people in Africa less?
I don't know much about the Nestle example, but in principle yes I think so.
I think the same would apply to any case where the production of each individual product does marginal harm. In that case a single individual can choose not to purchase the product and therefore have a marginal impact.
And maybe these kind of boycotts are more common than I suggested in the original answer, but it definitely applies to veganism.
But boycotts where you are trying to make a policy change require mass organization then?