Protests aren't trying to reach the people who've already decided they're wrong. They're trying to reach the unpersuaded masses who don't currently agree or disagree.

Obviously this requires the protesters to make a bit of a judgment call. Do I think the typical person leans so strongly towards my side that they'll take it when I force the issue, even if I annoy them? Sometimes the answer is no, and I've definitely seen people do counterproductive protests that way. But sometimes the answer is yes.