Chrome/Firefox: Facebook's privacy settings are, quite frankly, a mess. The only thing harder than figuring out what's being shared is deleting all of your activity. Fortunately, there are scripts to help with this.
As Business Insider points out, removing all of your Facebook activity can take hours. However, Absterge -- a script that works in both Greasemonkey and Tampermonkey -- can automate this process by deleting everything in your timeline. If you need more nuanced control, Facebook Timeline Cleaner performs a similar task, but Business Insider found it was a little wonky. Your mileage may vary.