Using such an app doesn't seem illegal. There is no magic trickery or privacy violation involved with such apps, it just looks at your friend list:
- Day 1: ask the FB servers for your current friend list and save it locally.
- Day 2: ask the FB servers for your current friend list again and compare this list with the saved list from day 1.
- Notify you about differences in the friend list.
This does not give you any information you didn't already have access to.
However. The app or extension needs to access Facebook with your permissions to access this information. There are ways to do this securely, so that you only grant the app access to your friend list. A browser extension is not such a way. A browser extension can bypass any security protections Facebook has implemented and can see everything you can see.
So while using this app might not be illegal, you should think carefully before installing it – maybe the app is doing something illegal with your access.