They're out of touch for thinking that tweeting this out wouldn't have consequences. Regardless of the validity of the criticism, publicly attacking your own employer is a stupid move if you want to stay there. I cannot sympathize
People should freely be able to have opinions on Twitter, Youtube, TikTok, CBS News, etc. and those opinions should not get them fired from their jobs just because some exec or some vocal group disagrees... as long as they're not representing the company. "I work for Pepsi and think the President is "..." for example.
On the other hand, unless it's whistleblowing, badmouthing your company to a broadcast audience when you don't have the imprimatur to do it, will most likely have consequences. Broadcast communications are the purview of The PR dept. This is for the PR dept to handle. You can opine it with your friends, family, etc. but not to a broad audience like that, unless you are considering the consequences.
That is an unrealistic take. Especially when the opinion is critical of the company. Much less when it's something as simple as the company not wanting to be associated with such viewpoints.
What They are normally not tolerated for is for maligning the company, institution or organization. That one should keep to friends, family, trusted people, but not something you voice in a megaphone of a public forum.