Is Orwellian Double-think Psychologically Possible?
When double-think is explained to mean

the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them.

It can be seen to be the same as repression in a sense, whereby one version of events is known, but repressed in favour of an alternative version of events, but it isn't repression in the true sense of the word when referring to the Freudian theory of ego-defence mechanisms.
When you look at my other answer today regarding the defence mechanisms, I pointed out that they can involve both unconscious and conscious thought processes and actions.
As for repression, it is a powerful ego defence mechanism whereby it can prevent a thought or memory which can be psychologically damaging from reaching the conscious.
When mentioning the interaction between O'Brien and Winston in your question, where O'Brien was trying to instil in Winton that some people didn't really exist when they did, I can see where the confusion lies when linking that to repression. The knowledge of these people's existence is trying to be altered by O'Brien and Winston was wanting to have nothing to do with it.
The key to the whole idea of repression is that it is a completely unconscious defence mechanism. When we deliberately and consciously try to push away thoughts, this is suppression.
Although some claim that suppression is a psychoanalytical myth with no scientific support, fMRI data suggest otherwise. For more on that, you can read Defense Mechanisms: Neuroscience Meets Psychoanalysis in Scientific American
Also:
Anderson, M. C., Ochsner, K. N., Kuhl, B., Cooper, J., Robertson, E., Gabrieli, S. W., ... &amp; Gabrieli, J. D. (2004). Neural systems underlying the suppression of unwanted memories. Science, 303(5655), 232-235. https://doi.org/10.1126/science.1089504
and
Bailey R, Pico J. (2020) Defense Mechanisms. In: StatPearls. Treasure Island, FL: StatPearls Publishing. Available free from: https://www.ncbi.nlm.nih.gov/books/NBK559106/