Safari extensions have suddenly stopped working (10.13.4)
The permissions issue ended up being the problem that prevented me from using extensions. 

For some reason, it keeps the weird time machine permissions (you can't edit a time machine backup etc.) when I copy over the Safari folder through Finder. It shouldn't do this and never has for me before this.

But I solved it by instead copying it over through the terminal, using cp, which doesn't preserve any metadata unless I specify that it should do that. After doing that, I had to reinstall the extensions (and thus lost some extension data) but at least they work now.

EDIT: I was able to recover the lost data, from a backup of ~/Library/Preferences/com.apple.Safari.Extensions.plist