It seems to make sense if a person posts opinions online but has no mention of where they work, there’s no intent there to be seen as speaking for the business, no way that can somehow be smeared onto the business they work at. No potential grounds for being fired.
I don’t see how they can be linked if they don’t ever make people directly aware of it. If they don’t then I don’t know how they could be.
One activity of Leftist activists is to try to discover background data about outspoken conservative commentators, and then harass the person’s employer. It won’t matter that YOU did not mention your employer. All it takes is for somebody knowing something about you and deciding to “out” you to the Left.
This is why I don’t use Facebook, and don’t even tell my wife what pseudonyms I comment under when online.