Hi classicalmusic.
I dont think having a facebook adds up to a “three strikes and you are out”.
There are many frum businesses and organizations that have a facebook account, as well as camps, etc., too.
I can tell you there are a lot of frum people who have facebook
accounts with nicknames or alias names. Whether it is harmless fun and keeping in touch with friends, or they are up to no good; depends on the individual.