Outside of your job though, the company you work for has no obligation to protect you as you aren't acting as an agent of that company on your own time
They can and will fire you for posting things they don't like on social media on your own time, whether you're right or wrong, though. With the justification that you ARE acting as a representative of the company.
If I had a dollar for every time someone got fired for saying anything remotely supportive about Palestine or criticizing cops for being bastards, I'd have enough to buy Boston.
They're right, though.