There is no definitive answer to this question as it largely depends on the jurisdiction in which you reside. In some jurisdictions, such as the United States, bingo games are considered an illegal gambling activity and are thus prohibited by law.
However, in other jurisdictions, such as the United Kingdom, bingo games are considered a form of social entertainment and are therefore not subject to the same degree of regulation.
Ultimately, it is up to the individual jurisdiction in which you reside to determine whether or not bingo games are legal. If you reside in a jurisdiction where bingo games are not legal, it is recommended that you refrain from playing them on Facebook.
However, if you reside in a jurisdiction where bingo games are legal, it is generally safe to play them on Facebook without fear of legal retribution.