Is it obligatory to delete every forbidden post in a Facebook group whose members do not abide by the prohibition of forbidden things within it, and is it permissible to relinquish its administration and appoint someone else to manage it?

You must change the evil with your hand if you are able. Enjoining good and forbidding evil is a communal obligation (fard kifaya), but it may become an individual obligation (fard ayn) if no one else can remove the evil. Accordingly, posts containing evil must be deleted. There is no objection to remaining as the group administrator or appointing someone else, provided that they prevent evil. Otherwise, close the page.