The analogy is either a serious misunderstanding of how the internet and web browsers work, or is a deliberate attempt to confuse these concepts.
> Why shouldn't I be allowed to vandalize a billboard
Because it's not your property. If you order a billboard and have it shipped to your house, you can do what you want to it.
> tampering with a server's software
What are you smoking? Do you not understand that a userscript runs on the client? The server isn't involved at all after it sends the HTML and JS files.
What makes you think you have a right to run software on my computer? You don't - I'll run whatever software I want on my computer. It's your business if you want to send me a page, of course. Just like it's my decision if I want to run some program.