Facebook security monitors users who have made aggressive comments, as well as former employees, through a “be on lookout” or “BOLO” list. It can use its apps and web sites to track the location of these people as it deems necessary.
Source: Facebook’s security team tracks posts, location for ‘BOLO’ threat list
I never used FaceBook (Android) app and I will never use it, until they release its sources under a license compatible to AGPv3.
It may not be enough thought, it may be necessary to pass through The Onion Router or proxies.