Bat-crap crazy is the less vulgar, publicly correct term for another term that is bat-sXXt crazy. They both mean the highest level of craziness, usually occurring impulsively and temporarily. You would use it to mean that something or someone is really, really not making sense, too crazy for words, a really dumb idea.
So my favorite TV character Sheldon is saying "Delightfully mysterious or really, really crazy?". As to the Facebook community, I did not know about that. However, if you Google bat-crap crazy, you will find a reference to the Democratic governor of Montana. He has called some legislation recommended by Republican lawmakers in his state "bat-crap crazy.".