Is the owner of a Facebook page accountable for the sin of users' female profile pictures, whether cartoon or photographic, who interact with his page, given his knowledge of his inability to prevent all types of non-female pictures?

A Muslim must be an aid to his brothers in righteousness and piety, not in disobedience, as Allah says: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression." Therefore, you must prevent violations such as images of women or images of 'awrah (private parts) on your page, otherwise, you would be a partner in sin. As for photographic and cartoon images of men, the preponderant opinion is that they are permissible, and there is no blame upon you for having them.