"people on Twitter should not decide who gets fired" is a totally different idea than "people shouldn't get fired for Tweets"! I agree that you shouldn't just be fired for having a tweet that's, like, controversial. But I think there are tweets that really are bad that one could deserve to get fired for, depending on the context.
And then, like you say, ultimately companies are going to do what they want to.
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And then, like you say, ultimately companies are going to do what they want to.