In the mid-1980’s I lived in Pattaya, Thailand where a pidgin English is spoken. I (and others) were soon speaking pidgin almost unconsciously. I suddenly became aware of this when an American asked me where I was from. “America.”
– You don’t sound like an American.
I drew a breath, and tried again.
– Now you sound American! 
That sure sounds annoying, if done without regard to the listener’s English ability, and fake accent to boot.
However in general non-native speakers in a language with limited ability tend to speak by translating literally from their own language. In case of Chinese speakers attempting English, since their language has simpler grammar and is generally more concise, the tendency is to leave out words and grammatical particles, verb endings etc. It seems plausible they’d also understand English more readily if the English speaker drops out those things, which English speaker hears as ‘broken English’. And it’s a common technique. Although I don’t know of a scientific study proving that it works, and again would seem to depend on the characteristics of the limited English speaker’s own language.
This made me think. The other day, something (I forget what) sparked my wife and me to briefly discuss speaking differently in different situations. She commented that I do that quite a bit. If I remember and things get quiet around the dinner table tonight, I’ll ask her what she meant. But I can see it happening.
I work in a professional field, which often requires that I speak and write precisely and fluently. I often interact with relatively unsophisticated people in my job, tho. While I don’t completely assume an artificial way of speaking, communication would be less effective if I spoke at my highest professional level. I hoipe I don’t do it in a manner that seems artificial or insulting.
In my personal life, I speak differently with different people. With most of my closest friends, well, they’re likely my closest friends because I am able to communicate with them on a relatively high level. But in less familiar interactions - such as with neighbors - my wife and I have previously been told on rare occasions that we spoke intimidatingly - like lawyers, when in our minds, we were simply using the most appropriate term for a given situation. So I think I intentionally speak somewhat more colloquially.
I know I’ve often heard of people from a cultural subset - such as blacks or Latinos, who will speak entirely differently in their social and familial relations than in their professional settings. I assume it is common - to some extent - with many if not most people.
I try and avoid using American colloquialisms. Non-native English speakers don’t get them. And we use a lot of them in everyday speech, especially when we try and use humor. Yes non-native English speakers will laugh along with you, but they normally have no idea what the joke is.
I do this a lot. I’m not a native English speaker myself, but my English is fairly good and I use it on a daily basis. But, like I said, I often find myself talking to someone who doesn’t speak English that well and will quickly adapt to that. Simple sentences, only present tense etc. It just makes communicating easier, although sometimes I underestimate the person I’m talking to and she/he will correct me (rightfully so). Which is always good for a laugh.
For what it’s worth, I’m equally often on the other side of the interaction in a language I hardly speak. There is such a big difference in the way I’m able to converse with people. Some keep it relatively simple and we can speak (well," interact" is a better description) for hours in this language I barely know. Others seem to choose only words/verbs I don’t know and exchanging names can be a hassle.
Not so long ago I read an article on the BBC website (can’t seem to find it now) that discussed how native speakers may cause many problems in international business settings. By using idioms, understatements, etc. the message often fails to land. In such a setting with dozens of nationality, it is often the native speakers that cause confusion, while the non native speakers are very direct and understand each other quite well. Interesting read!
Predominantly, no. I speak in the most-correct English that I can. I assume that, since their mastery of my language is ongoing and developing, it’s my duty to do it the right way. I’m sure there are exceptions… I’ll try to pay attention to that during my conversations next week.
I have started to slow down and use fewer obscure words that they may not be familiar with. That is, unless I’m hanging-out, in-person with them. Then the challenge is on. My English-as-a-second-language friends have commented that they appreciate learning the new words and idioms.
Related: When i’m hanging-out with my home-grown, english-speaking redneck friends, my vocabulary and syntax will change accordingly. This is done for fun as much as acceptance.
This is the proper approach. Do not speak broken, incorrect English. I have heard people do this to non-native English speakers and it drives me crazy. Sounds condescending. Just speak slowly and keep it simple and the listener will probably understand.
And it’s the same for me. I can understand German much better than I speak it, so I appreciate if someone must speak German that they do so slowly, but not incorrectly.
Like previous posters said, moderately slow speech, simple sentence construction, and clear pronunciation is best. And avoid idioms. Idioms are so insidious, though, that you don’t realize you’re using an idiom until you stop and think about it.
This was my policy as a college professor where I encountered non-English speakers regularly. A lot of people can understand a foreign language better than they can speak it. So trying to adjust to their speaking level is overkill.
Contrasted to idioms, using more technical terminology in that context helped rather than hurt.
Like others, I speak slowly and use simple phrasing if someone has difficulty understanding me. But I would never speak broken English. In addition to being patronizing and cringeworthy, it probably would impede rather than facilitate communication.
I am used to modifying my speech, since I teach a foreign language to university students. Obviously, I am concerned with modeling correct grammar for my students in a way that is unnecessary if you just have casual contact with someone. However, there are all sorts of strategies to assist the listener in understanding what you are saying: paraphrasing, repetition, visual cues, etc.
In international business, idioms were the bane of my existence. The VP of international sales, of all people, was one of the worst. Sales people tend to be good at speaking, which normally means using interesting language but for heaven’s sake, stop it!