I'm assuming the "fuck you" was the one that fired her. However you choose to understand free speech, being needlessly rude as a media representative of a company should get you fired.
Assuming accurate reporting, in the absence of a social media clause that, when shown, your boss agrees you don't need to sign? Doesn't pass the sniff test.
(Curiously, I've just seen someone walk past me with "duck off" printed on their T-shirt. But then, culture here in Germany is much more liberal about both word and deed — it's American cultural norms that made the autocorrupt inside my quote marks).
Given the tweets and the article, it's fair to assume that this is not the first time the person has exhibited such behavior and this was just the last drip overflowing the bucket.
(Curiously, I've just seen someone walk past me with "duck off" printed on their T-shirt. But then, culture here in Germany is much more liberal about both word and deed — it's American cultural norms that made the autocorrupt inside my quote marks).