I am the only full-time monolingual employee of the company I work for, the only one who does not speak Mandarin, the only one whose mother tongue is English, the only one who grew up in a primarily English-speaking country, and one of maybe four who would be classified as fluent in English (and that count is probably high).
You can't imagine the things that pass through my inbox every day. I've worked for this company for years. This would be impossible were I not understanding of the failings of non-native speakers.
But when I need to correct their formal English (not often, because it only occasionally matters, since our target market is mostly Chinese), not one of my co-workers dismisses it out-of-hand. They know their limits, and immediately seek to understand what is going on, rather than ignoring the issue.
This has been my (much more limited) experience with non-native speakers from other parts of Asia and Europe, as well. Encountering a non-native speaker who does not behave this way is rare, I can think of only twice that I've personally run into it, and both times it involved people who had severe interpersonal issues well beyond language.