I used to work for a company whose guidelines for employees included “Assume the best of intentions,” and I’ve taken that to heart with colleagues and clients ever since.
One of my colleagues writes very terse emails, and when I first started working with him I was concerned that I had angered him, so I called to see how I could set things right… only to find out that he wasn’t angry after all. He writes very directly because 1) for him, that’s how he makes sure his writing looks professional and 2) he learned written English with the purpose of communicating business needs, and finessing messages with friendly American style is harder.
So I’ve learned to read his emails like I would an instruction manual: impersonal and direct but not antagonistic. It takes me less time and effort to do this than he would need to reach the level and attitude of a native speaker.
Assume your non-native-speaking colleagues have the best of intentions and are trying their best to communicate, and things will overall go much more smoothly than if you take things as a personal affront or try reading nefarious purposes between the lines.