People obviously have only one identity, and that has to cover them for both work life and personal life. Asking people to totally sacrifice a private life in favour of work is unreasonable.
This isn't such a problem offline, but when everything is written down online, the scale of the problem makes it a whole new issue. It’s easy to see how an employer could worry about what staff may be writing online, but this does not give them grounds to tell you to stop using the service in general.
What they can sanction you for is anything you do that they have a reasonable belief could prove detrimental to the company.
If they can prove that your conduct online has caused detriment, they could take disciplinary action against you and potentially dismiss you as a result. Depending on the detriment, they could also sue for damages.
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