No extension is needed. (I never use extensions for anything.) Unfollowing all friends is not complicated and can be done in a couple of lines of shell script, or using whatever programming language or HTTP client one chooses. Obviously, curl would work. There are a hundreds of ways to send HTTP requests. It is a very simple protocol. No POST requests are even necessary, only GET.

1. Log in to Facebook

2. Open "Developer Tools" (F12), select the "Network" tab, locate "Request Headers", Alt-click on "Cookie:" and select "Copy value". Use this in each HTTP request. Do not log out yet.

The URL for the Friends list is

   https://mbasic.facebook.com/friends/center/friends/?ppk=1

where 1 is the page number.

Using m.facebook.com as the domain will also work. There 10 friends per page.

3. Extract the UID for each friend from the HTML and create the new "unfollow" URLs.

   grep -o "uid=[^&]*" 1.html|sed 's>uid=/https://mbasic.facebook.com/a/subscriptions/remove?subject_id=>'

4. Log out.

Done.