I'm not familiar enough with other cultures to answer the question but I have a perspective that I haven't seen expressed in the comments or answers. The other answer also proposed a predictive system rather than providing direct answers1, so I thought I'd weigh in.
Stigmatizing an honest attempt to use original-language pronunciation can be a reaction against prescriptivism motivated by reverse-classism/anti-elitism. The prevalence of this phenomenon will, I suspect, be primarily affected by a given society's attitude to class. However, I don't believe that this is precisely what's being portrayed in this video.
There is a reasonable argument in support of Mike Trapp's (the "over-pronouncer") actions. He claims that "he's not imposing his Anglicized pronunciations on these foreign words.".
If you believe that the English word "café" and the French word "café" are one and the same word rather than cognates2, then it's not unreasonable to claim that "the language that invented this word should be the authority on how it's pronounced". His claim that it's "less racist" might be supported or disputed by the actual speakers of that language (especially - see my aside, below). However, "embarrassment at being adjacent to a racist action" is not the only consideration of why a bystander might react negatively to using original pronunciations.
Familiarity with foreign languages is a privilege - one usually granted by education, itself often (not always) an indicator of wealth. Using original-language pronunciations can therefore be seen as an arrogant demonstration of privilege and/or an effort to differentiate oneself from the uneducated. "I'm better than you because I know another language <because I am wealthy enough to have been educated enough to learn it>". This is similar to the single-language case of prescriptivism being used as a tool of classism - "I'm better than you because I employ the
Subjective Subjunctive mood 'correctly' <because I am wealthy enough to have been educated enough to learn it>" isn't the same assertion, but it rhymes.
Bystanders to an original-language pronunciation might be embarrassed or hostile towards it not because it's seen as racist (though - again - see below), but because it is perceived (accurately or not) as an insulting attempt to "claim class". Assuming that the listeners consider themselves of a similar class to the speaker, they may be insulted that the speaker thinks themself superior, or (in groups that have strong negative feelings towards the upper class) they may be hostile to someone attempting to enter the upper class.3
As an aside, though, I do not believe that "Using original-language pronunciations is either funny or embarrassing" is "The 'point' that the video makes". Go watch the video again. Notice the stereotypical Italian "finger purse" on "Linguiiiiiiine", or the exaggeration of the rolled-"R" (a stereotypically Spanish sound) on "Conquistadorrrrrr".
Mike's pronunciation here could be seen as offensive4 because it reduces a language to stereotypical traits. His friends are here embarrassed because they guess that other guests might be offended by this exaggeration of stereotypical accents, not because they guess that other guests might take offense at his social climbing or bragging about education.
If you use the actual foreign language pronunciation of a word, in a moderate approximation of the original accent, you're taking a gamble - you might be seen (as Mike hopes to be) as open-minded, humble, and respectful, or you might be seen as a social climber. But if you demonstrate disrespect for a culture by caricaturing its accent - if you "over-pronounce" - you're always an asshole.
1: I'm new to this particular site, so I'm not sure of the answering-etiquette. Apologies if I slipped up!
2: An interesting philosophical tangent, especially when they start being used with different referents: "Nirvana is an English band, but it's a Hindi word
3: There's an alternative case where the speaker attempts to ingratiate themselves with a person of a higher class by using "hypercorrect" language. If the higher-class person does not themself use that pronounciation, it might be seen as gauche or embarrassing to have "tried and failed" to claim class. I suspect, though, that this case is much rarer, and is not what's being portrayed in the video.
4: Note the intentional use of "Could be", not "Is". I'm not going to speak for what's offensive to anyone else, of any culture.