Not everyone on facebook lists their faith, you cant really know who is who, what profile is fake, even with ppl that do provide a lot of data.
Sure, a nazi type of government doesnt need to make absolutely sure, but you cant really defend yourself against those anyway.
When being muslim will be a reason for departation/internment in isolation camps like the japanese were in WWII for instance, the gov't will have a hard time proving ppl are indeed muslim in many cases, even if their facebook profile says so. Whether they will need a solid proof or not, that is the real question. If they dont, nobody is safe, your neighbour might say you are muslim just because your backyard tree is too high and casts shadows on their lawn.