There's a famous paper called [DO POLITICAL PROTESTS MATTER? EVIDENCE FROM THE TEA PARTY MOVEMENT](https://www.aeaweb.org/conference/2013/retrieve.php?pdfid=22...) that addresses these concerns. They use the weather as a proxy for randomized controlled trials and show that: areas where it rained during the tea party protesters had fewer protesters and the tea party movement had fewer votes in those areas. Because weather is essentially random, we can therefore conclude that the fewer votes was probably due to people choosing not to protest due to the rain, and if they had chosen to protest then there would have been more tea party votes.