Elected officials' online anti-vaccination statements respond to online engagement

State legislators play a central role in U.S. vaccination policymaking, yet little is known about how social media engagement dynamics structure elected officials' online anti-vaccine messaging. We examine whether public engagement with lawmakers' anti-vaccine posts functions as a behavioral feedback loop, characterized by subsequent production of anti-vaccine content from those same legislators. Using a large-scale digital trace dataset of tweets from 2,619 state legislators in 2021, we identify 83,130 vaccine-related tweets and 3,314 anti-vaccine tweets via transformer-based text classification. We model anti-vaccine posting at the legislator-month level with an integrated set of individual, state, and temporal predictors, including partisan time trends and state-level pandemic conditions. We find that greater engagement with prior anti-vaccine tweets is associated with a higher probability of posting anti-vaccine content in subsequent months. We further show that replies tend to mirror the stance of legislators' vaccine-related tweets, suggesting that public engagement can amplify legislators' perceptions of audience agreement, sustaining continued anti-vaccine communication. Additionally, anti-vaccine tweets are more likely than other vaccine-related tweets to link to low-credibility sources, indicating that engagement-driven reinforcement may facilitate the circulation of misleading information. Overall, these findings illustrate how public interaction with social media platforms' engagement architectures shapes elite political communication and the informational politics of public-health governance.