It's completely expected for a company to get rid of individuals on the payroll who are badmouthing the company they work for.
Why would anyone willfully employ people to work against the company's interest?
It's the same old discussion about whether something is right just because it's legal or allowed. Just because a company has a right -- and an incentive -- to do something, doesn't mean that's a morally or ethically right thing to do.
In my opinion, what Whittaker is doing is, in a way, analogous to civil disobedience. And, just like with civil disobedience, reprisals are expected. It's worth keeping in mind that those reprisals aren't automatically right by virtue of being expected, just as her actions aren't automatically right by virtue of being similar to civil disobedience.
In other words, some of us feel we can't afford to, as another commenter put it, "leave your politics at home and let me do my job in peace". I believe this attitude -- that science and engineering should somehow remain orthogonal to and decoupled from ethics and morality -- to be downright pernicious to the society.