HR stops you from doing that. Publicly bad mouthing the company you work for is definitely grounds for termination. If it was any other company in any other state it would have happened quickly and swiftly. It wouldn't be a news story.
Having not read any of the tweets in question, I can not say what the content is about.
However, according to https://www.hg.org/legal-articles/can-you-fire-someone-for-t..., speech about working conditions and union organising is protected.
I suspect none of us armchair lawyers will come up with a simple way to analyse these tweets with a lot of context that isn't available.
We aren't talking about termination on that ground though. We wouldn't have this discussion here if it was, I would actually agree with it (though I would still find it sad that the company wouldn't try to improve what an employee see as an issue).
> HR stops you from doing that.
Here's the exact quote from the comment I was answering to:
> You cannot accept a paycheck from a company, while also be trying to subvert it internally.
We weren't talking about "Publicly bad mouthing" but about "subvert it internally", or in a less threatening way "changing how the company works internally". I believe you have all the rights to do this even on its paycheck, it's about improving what the company does, which is pretty much what employees are paid for.