The issue is not about making a political statement.
As an individual, you should always have that right.
Both the New York Times and Breitbart are purveyors of propaganda for their respective political parties. They literally do nothing but make massively biased political statements, all day long.
Imagine you work there, and you disagree.
You can totally try to change that from within. Fight the system.
Work your way up. And once you have sufficient stature within the organization, you can run, say, an article praising George Washington on the front of the NYT, or a piece condemning him on Breitbart.
But, you, as a journalist, are a public face for your respective brand, and as such, you will likely face disciplinary action for going against the brand image.
It doesn't mean you can't make a statement.
But when you leverage your employer's platform to do so, there are going to be consequences.
Now, if you use your own megaphone, you absolutely deserve protection from being fired!
Build your Twitter/Instagram/Facebook following, and preach as much as you'd like. You built it. It's yours.
That's the reality of being a public figure. You are paid to be part of a brand image.
Tell me where I'm wrong on this. Or where you think we should draw the line. I'm happy to hear other opinions.