Answer:
In general no. It depends on what you post on social media. But what should be looked at is what you do at work. Are you rude to the customers, are you helping, do you lose money or earn it and so on. If you post some really immoral but still legal things like Nazi propaganda and things akin to that then you could seriously hurt the image of the company and many things that this kind of posting could justify being fired. But if you are posting jokes about your boss, not liking your boss or anything like that then the boss should not have the power to fire you for just not liking the fact that he is being made fun of.