Answer:
With privacy laws put into place, it's not ethical for employers to view personal information through emails but is absolutely possible if need be, provided that the employer has a solid policy in place informing employees that no information sent or received on company equipment is private.
I personally don't believe that a company should fire an employee over a social media post UNLESS what they're doing is illegal or dangerous. However, employers can fire employees for anything, including their social media posts.