It seems to me that when people say that we only believe what we want to believe, they're usually talking about other people. Or more specifically : other, stupider people. Clever, smart, wise, rational people are those who by definition aren't so easily susceptible to their own preferences.
This isn't wholly wrong. But it's worth remembering that things are a good deal more subtle than that. For one thing, confirmation bias may or may not lean towards what we want to believe rather than what we actually do believe (which are not always aligned). For another, it's emphatically not only about stupid people. For example in the tension between different measurements of the Hubble constant :
The calculations using Cepheid stars still give higher numbers, but according to Freedman's analysis, the difference may not be troubling. "The Cepheid stars have always been a little noisier and a little more complicated to fully understand; they are young stars in the active star-forming regions of galaxies, and that means there's potential for things like dust or contamination from other stars to throw off your measurements," she explained. To her mind, the conflict can be resolved with better data.
"That's the way science proceeds," Freedman said. "You kick the tires to see if something deflates, and so far, no flat tires."
It isn't only stupid people who believe in unicorns - which seems to have become a popular term for wanting magical things that can only be obtained through paradoxes. Johnny Foreigner, a.k.a. Schrodinger's Immigrant, is perhaps the best example of this : an expat who simultaneously comes over here to both steal our jobs (because he's willing to work under any conditions for practically nothing) and our unemployement benefits (because he's a lazy, good-for-nothing slob who's willing to go to extraordinary lengths not to lift a finger).
I would suggest that cosmologists aren't anywhere near that variety or level of stupid, but they too yearn for a unicorn of sorts. They too have conflicting, mutually-exclusive desires. Practically every scientist would love to find some genuinely revolutionary physics that would overthrow all those other dogmatic fools - that's the whole, undeniable point of the job. Equally undeniably, we also want the hard-won established models to succeed... we don't want to throw them away unless we have to !
My take is that this is another examples of how are brains aren't always Bayesian nets. When we establish something, we don't automatically discard all (or even any) of our older, now-conflicting opinions. Likewise we can want things that simply can't co-exist, but we want them anyway. I personally would bet heavily on the Hubble tension being a sort of measurement problem, so I want the Standard Model to be true in that I want to be right (who doesn't ?) but I also want it to point to a properly spectacular revolution (again, who wouldn't ?). We have different reasons for different desires which can make them horrendously irrational.
This does not put cosmologists on a par with unicorn-hunting Brexiteers, of course. But we'd do well to remember than even very clever people can be as dumb and stupid as the rest of us - or at least, their motivations and desires are just as irrational as those of anyone else. Only if we take the time and trouble to consciously examine what it is we really want do we have any guarantee of self-consistency. This is not (only) because we're idiots. It's just part of human nature.
Cosmologists are definitely nothing like brexiteers, cosmologists haven't been blocking imports of critical scientific equipment since January. As I understand you're in theoretical astrophysics/astronomy, but if you have any colleageus in experimental fields you'll see how angry we're getting. Just listen for the sound of heads venting steam in the next door office when we hear that the single global supplier for X is "no longer shipping t the UK because of brexit border complications".
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