Vincent - Social media usage is very subjective as some workplaces have clear guidelines and do's and don'ts associated with it. Does your organization have any such policies? Initiating legal action would depend on the internal complaints management process, what steps were taken to warn employees, and how the situation improved or how employees responded to your questions/concerns.
A blatant legal action may not be warranted as this seems to be a case of personal remarks that employees make as part of their informal circles on social media platforms. If you have ulterior posts from employees on social media platforms, this is very concerning and may be taken up with the concerned employees in involvement with HR, Operations/Business, and the PR Team to assess the gravity of effects it will have on the reputation of an organization.
So, it is completely subjective. There cannot be one final guidance on this.
For a list of cases on social media abuses, there are ample litigations going on related to rights on social media platforms. You can simply search it online.
Practical advice - It is important to have the PR and social media usage guidelines drafted and circulated for your organization that will serve as a standard across. Also, the policy should include the complaints handling procedure, including those from the employer's side.
Thank you.