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Americans in particular seem to assume that issues fall along the same political Dem/Rep divide as in the US.

Yes. As someone who grew in Russia, if I'd talk freely and casually about politics in the way we do here, with Americans IRL nearby, I'd probably be literally lynched regardless of those being majority Democrat or majority Republican minded, and if those Americans were sufficiently inattentive, even by a mixed crowd. Things associated with freedom and dignity and just human treatment of each other here are associated with fascism there, and the other way around. And it's very counterintuitive. And also honestly Americans and continental Europeans (but not Brits) generally feel more like peasants with pitchforks than like Russians, in every political-minded discussion. It really feels that they'd be perfectly fine with everyone disagreeing being relocated six feet under, and the purpose of the discussion is usually to let you atone and ask for mercy. Despite all the stereotypes about Russians, this is not the case here, you might get insults, but not that heavy unwillingness to accept your side's existence.

Though that was 10 years ago, now in the Russian-language space there's much wariness of propaganda and legal problems for speech and so on, so people speak less freely, while a loud minority of bootlickers likely outside Russia repeat some combination of American points, more similar to a Republican set, but at the same time certain they'd be loved by Democrats. It's weird.