I have a working module on linux and one of the client wants it on windows. There is very good discussion on similar topic here(https://ask.slashdot.org/story/04/08/12/1932246/cygwin-in-a-production-environment), I guess it leaning towards avoiding cygwin for productions but its about 13 years older discussion,there might have been issues but in about 13 years I hope cygwin might have been improved,matured and good for production use.
The code compiled just fine and seems to work ok under cygwin so its very tempting to take it forward rather than redoing it in windows native code. But if there are really any unsolvable known issues and people are avoiding it for productions I would like to know. The code heavily uses pthreads,sockets in no-wait
I've used Cygwin a fair bit, and have found it mostly unproblematic. I am aware of some of the reported problems, but haven't experienced them myself. Some things on Cygwin are much slower than the same code on Linux -- I notice this most with directory scans, but that probably isn't the only thing. People complain about fork() being slow, but that isn't really a surprise, as 'forking' isn't a native concept in Windows. If you're just using fork() to launch subprocesses, then conceivably the whole fork/exec thing could selectively be replaced with calls to native Windows APIs.
A potential limitation of Cygwin is that it requires Cygwin at run-time or, at least, a chunk of Cygwin infrastructure. MinGW might remove this restriction, but at the cost of leaving you to make a larger number of compatibility-related changes in your code (file locations, for example). The last time I looked, MinGW didn't have tooling as extensive as Cygwin, either, but it's probably good enough for many purposes.
I guess another possibility to consider these days is the Windows Subsystem for Linux (WSL) on Windows 10. I've found that code that builds for Cygwin usually builds and runs without changes on WSL, but I haven't really figured out what the relative advantages and disadvantages of Cygwin and WSL are.
I've not noticed problems with pthreads in Cygwin, MinGW, or WSL; although I guess any problems are likely to depend on the exact way you use threads. I can't comment on the no-wait socket issue, because that isn't something I've tried.
Incidentally, both Cygwin and MinGW will allow you to call native Windows API, and other functions in DLLs, if you need to. So the possibility exists to create a sort of "hybrid" application that uses POSIX-type functions and also Win32 APIs. This might be useful if it turns out that some things are much faster with Win32 functionality. I'm not sure this is possible with WSL.