If Umbridge believed that Sirius was working with Harry, how could she believe the official story - that he is a Death Eater?

Question

Chapter 28 of Order of the Phoenix makes it extremely clear that Umbridge believes that Sirius Black is working with Harry Potter.

“Mr. Potter,” said Umbridge, “let me remind you that it was I who almost caught the criminal Black in the Gryffindor fire in October. I know perfectly well it was you he was meeting and if I had had any proof neither of you would be at large today, I promise you. I repeat, Mr. Potter ... Where is Sirius Black?”

However, this is a clear contradiction of the official story, that Sirius Black is a highly ranked Death Eater. For example, the headline of the Daily Prophet article on the Azkaban breakout was "MASS BREAKOUT FROM AZKABAN MINISTRY FEARS BLACK IS "RALLYING POINT" FOR OLD DEATH EATERS" (OotP, chapter 25) and this article had several quotes from Fudge supporting this view.

So, do we know what Umbridge actually believed? I can't see an easy way to believe both of these at once.

Answer 1

It's called Doublethink, although the Wikipedia article describes it from the meaning as it applied to the proles and the Outer Party; they were expected to believe contradictory things, simultaneously, without question.

The doublethink practiced by the Inner Party took the form of believing one thing at one moment, and believing a contradictory thing at another moment, all for the expediency of the moment.

Note that in 1984 much of the vocabulary of Newspeak was deliberately ambivalent. Depending on what the Party wanted at any given moment, the neologisms doublethink, blackwhite, or duckspeak could mean completely opposite things, depending on the context; and the Party had no difficulty ignoring that context if it suited them to go after someone for something he had said.

Umbridge is exercising the second form of doublethink, and at every turn it is done in order to gain or retain power, just as the Inner Party does in 1984. She parrots the Official Truth—that Sirius is a Death Eater—in order to preserve her position in the Ministry, but when she is going after Harry she does a one-eighty on this and assumes without pause that Harry might be working with him.

TL;DR: The desire for power is illogical. Don't expect people who want power to be logical.

Answer 2

Dark Lord Harry

However there is a second option which could allow Umbridge to hold both the belief that Sirius is a Death Eater, Voldemort isn't a problem, and Sirius is in contact with Harry at the same time without contradiction.

We might remember what Snape told Bellatrix and Narcissa about Harry in Harry Potter and the Half-Blood Prince. Namely that there were rumors that Harry could only have defeated Voldemort by being a powerful dark wizard and could be "a banner we [Death Eaters] could rally around." These rumors were circulating around long enough that Snape used this as a (apparently believable) excuse for why he didn't instantly try to kill Harry. So at the point Umbridge is asking Harry about Black, it's only 5 years since "Harry could be a new Dark Lord" was a thing people were actively discussing. Voldemort in this scenario isn't a big deal for Umbridge, because the ministry thinks he's gone forever. Rumors of Voldy are just a cover for Dumbledore to gain power.

If you take that "Harry could be a new Dark Lord" rumor as true, it makes sense that Sirius could be trying to get back to Harry. (The ministry likely suspects Sirius escaped with Dumbledore's help, and he is known to be Harry's godfather.) After all, Voldemort is gone, so it makes sense that Death-Eater Sirius would go to his godson-the-new-dark-lord. Is Dumbledore using Dark Lord Harry to rally old Death Eaters to his new cause far-fetched? Yes absolutely. But it makes enough twisted sort of sense that it could be Umbridge's reasoning, especially if she refuses to believe the Ministry could actually be wrong about anything.

My personal belief is that Umbridge did know Sirius wasn't a Death Eater, but was a Dumbledore supporter and therefore she could use popular opinion that Sirius was an escaped Death Eater to get to Harry. But you asked for a plausible reason for Umbridge to believe that Sirius is both a Death Eater and working with Potter.