Should Employees be punished for what they post on social media ?

Recently saw a post where a girl who’s started working got fired from her job due to some drama between her and the a RW mob on X and they kept tagging the company and forced her to be terminated. Haven’t really dived deep to check what the actual matter is but my point here is that should companies take action against employees for what they do on social media which doesn’t really involve the company.

Are there laws regarding this or anything mentioned when we join a company and does this set a bad precedent which jeopardises free speech ?