interestingly a recent defamation case actually holds organisations to account for comments on their pages. individually it's obviously different but it is a step in the right direction.
My recommendation is that any organisation that is public facing with public facing employees that are in and scrutinised by the media, everyone has a verified profile (blue tick) with all content moderated and signed off. Players can have their personal profiles, but on private and only for close friends and family. Community and social media specialists are hired exclusively for the moderating and managing of these profiles.
From a branding perspective it is a no brainer but also for the sake of PR, publicity, AND player wellfare it controls the story, the imagery, the message, and the engagement. As a society we still see social media as a "private" thing and thus people and players should have a "right" to engage safely, free from toxicity. It can be approached that way but atm players basically for the most part have free reign, and they are opening themselves and the club to all sorts of trouble, as we have seen recently with these racist posts. In essence the club is liable here because it hasn't fulfilled its obligation to both prepare and train players for this sort of stuff, and basically allows it to happen. Relying on government and social media outlets to protect them from this stuff is futile. The resources are there to take full control and to shield players from this stuff. The approach needs to change.