As long as the person posting in no way associated himself/herself with the business, then sure, leave them alone.
If that person identifies in any way where they work, then fire them for probably insulting at least half of your business base.
LOL!
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.