Question for everyone on the use of “public” property

https://nypost.com/2024/10/14/us-news/massachusetts-town-issues-cease-and-desist-to-resident-projecting-trump-sign-on-town-water-tower/

In this story, a person is projecting a political sign onto a town’s water tower. The water tower is “public” property. I am well aware that the goal of an-cap is the ending of a state, which would mean there would not be “public” property, only private. And I’m also aware that an-caps would not promote any statist leader, let alone one over another.

I’m curious what people’s thoughts are from an an-cap perspective though. Is the person projecting the sign in the wrong because they are projecting onto something that is not their own personal property? Or do you feel that since it is “owned” by a state entity, and the state should not exist, that it is allowable? If it helps, imagine it’s not a sign promoting a politician, but could be anything.

I’m not as concerned with thoughts on the town’s response, more-so on the individuals actions.