I'll provide an exact account of what I'm trying to do, in case the answer can vary depending on the plug-in.
At work, I've installed the Feed Intent Viewer plugin without incident [With the latest Chrome version].
When I wanted to install the same plugin into my Chrome browser at home, I was prompted to sign in to Chrome. When I refused to do that, the browser didn't allow me to install the extension.
I was signed in in neither of those cases, yet I was able to install an extension in the first case and not in the second. Why? Can I somehow work around it?