So, first, I don't think Google search is harmful, so I'm not especially interested in boycotting, but I'm happy to grant this for the discussion.
There's already an interesting question about when boycotting is it worthwhile tactic, but in this situation, there's the additional complexity of there being two ends at which one could boycott a search engine:
* Producer: don't allow the search engine to include your stuff
* Consumer: use a different search engine
This is not the only place you find this dynamic. For example, if I thought Chrome was harmful, I could choose:
* Producer: make my site incompatible with Chrome and suggest people switch
* Consumer: use a different browser
Or, with email:
* Producer: don't email people with @gmail.com addresses
* Consumer: use a different email provider
Thinking through these cases and similar ones, if you think Gmail / Chrome / Search is harmful then the "consumer" side makes sense: the alternatives are nearly as good so you're not giving up much, and you're helping increase diversity. On the other hand, the "producer" side ones are much less attractive, because they're a much larger sacrifice and the benefit doesn't seem that big.
(Disclosure: I work at Google, but not on Search, Chrome, or Gmail)