Shameless plug, I wrote a plugin for Chrome [1] and Firefox [2] to do just that.
(Facebook is the opposite of WhatsApp – you can disable your online/offline status, but not your idle time.)
[1] https://chrome.google.com/webstore/detail/social-network-cha...
[2] https://addons.mozilla.org/en-US/firefox/addon/social-networ...