There is a specific context though, that makes the propaganda far more believable to many Russians than what they read online through VPN or - for most Russians - through word of mouth.

I watched a Russian elderly lady, who appeared like a decent person, respond to a western journalist. She said that she knew for sure that the news from the West were untrue "when they said that Russians troops were shelling Kiev and Kharkov - which is impossible".

Many Russians - most in fact - consider that Ukraine is historically a part of Russia. Which is untrue, but that's "common knowledge". So Ukrainians are their cousins, their brethren.

Hence the syllogism: if Putin has sent the Russian army to Ukraine, then:

1/ it doesn't make sense to kill civilians and shell cities to the ground

2/ the attack must have valid reasons ("Nazism", existential threat to Russia by joining the USA' side through NATO, ...)

When you are in such representations, believing Putin's propaganda is quite rational.

By the way, we should also be more skeptical of what we are told on our own channels. Our media are relying all the time information they get from the US government, the British intelligence and the Ukrainian government WITHOUT any possible way to cross-check them.

No journalist can cross check the idea that Putin is being lied to by his generals, by his entourage and by the FSB. It is quite possible ; it would explain a lot of what happened during the last month ; it is logical since despotism reign by fear - and truly we have all seen how fearful these people appeared to be during the televised Russian security council.

But our journalists are relying what our governments and the Ukrainian government say, without verification. Most mention that fact, directly or indirectly ("according to...") - but they five credit to this narrative anyway by propaging it.

Russians are wrong to support this unprovoked and atrocious invasion of Ukraine - but they are rational, not gullible or escaping a disturbing reality because it's easier to cope with, even unconsciously.

Humans are rational. Russians are rational and we are too in the West.

A good reading about this: "the Savage Mind", 1962, by the anthropologist Claude Levi-Strauss. He demonstrates that Natives' way of thinking in the Amazonia was as rational then as we are today, as were people in the Middle Age or ancient Greeks or ... jihadists from All Qaeda.

Not that I like it - but just let's stop with the ideas that people we disagree with are not rational.

Even Flat Earthers are rational people! It sounds absurd at first but it's really not. The Enlightenment movement of the XVIIIth century was precisely of discuting everything that was proclaimed as a Truth in common knowledge or by authorities (the Catholic Church, ...).

It's not irrational to think that Earth is flat. Most of our day-to-day experience tend to prove this idea. Demonstrating that Earth is a globe is not that easy. It's easy to make simple experiments that hint that Earth is not flat, but explanations can be found to explain the discrepancies. Really proving to people that Earth is round without a mediation like films from space is not easy. Of course, the Flat Earthers are prone to detect conspiracies everywhere, so they discard the films as fabricated. Which is not irrational. The proof needs either a direct experience in which Flat Earthers would have total control, or a decent level in Mathematics and Physics. Most of people who are right to think that Earth is a globe don't know how to replicate the proof of it. They believe what Science says - which is a very rational attitude.

The only way to change the mind of most Russians is to find people they trust (for any reason), send those to Ukraine with cameras and have them do their independent reporting. Showing the atrocious results of Putin's invasion, eg massive civilian casualties, destruction of whole cities, war crimes, ..., will create the emotion that humans need to reconsider what their rationality led them to think.

Humans don't change their mind when confronted to a "rational presentation of facts". They need a strong motivation to accept to reconsider. Only emotions can provoke the shock required.

Many experimental psychology studies have demonstrated that "rational demonstrations" by scientists to whatever-believers (antivax, ultra-nationalists, jihadists, flat Earthers) lead to ... the reinforcement of their beliefs.

Our rationality is driven by our emotions. Which doesn't mean that we are not rational. Many scientists complain that they are perceived as super cold people, which they are absolutely not. But their very core of their job is to chase their own biases all day long. And that's a difficult task. Hence the crisis of reproducibility in many fields of Science, where the "publish or perish" tyranny nudges scientists to get results all the time. Some of them are just manipulators, of course, but the crisis of reproducibility is much deeper.