This article doesn't really have anything to do with the Washington Post, and it's not any more about WaPo than any other twitterer. It's an opinion piece that happens to be by one of the Washington Post's stable of writers, but she has no more say over their policy than you do.
Editorial pieces are chosen to be printed by the news group. While it "might not represent [news group] opinion" it usually does unless the topic is not meaningful to the news group. This seems like a pretty basic strategy to me -- my high school current events teacher would always remind us to "consider the source". Is this really controversial?
This isn't an editorial. It's an opinion piece, by a regular columnist.
They get printed on the same page of the paper, but they have a different relationship to the newspaper itself. The editorial staff work directly for the paper, and have a fair bit of say in its operations.
This is a regular columnist. The news group didn't select this piece. They just ran the text in the (probably weekly) slot reserved for this columnist. They did hire her in the first place, but not because she reflects their opinions.
Columnists are hired specifically not to repeat what the editorial staff would say. They often represent a diversity of opinions. More relevantly here, they get to work independently: they produce their material without oversight of the editorial staff.
Their actual hiring structure can be complicated. They may be syndicated, or they may get their paycheck directly from the newspaper. But either way, they don't have any control over the newspaper's policy. The only power they have is to put words on the page -- an important platform, no doubt, but the newspaper doesn't have to listen to them.
There are more left-leaning ones than right-leaning ones, but it's a diversity of viewpoints.
Whether they should leave Twitter is, in theory, apolitical (though nothing is apolitical even more). I have no idea if any of the other columnists have an opinion one way or the other.