Preventing Cygwin from picking up MinGW as host system

[Ilmari Lauhakangas]

So this beautiful annoyance came up during an email-driven 
troubleshooting session:

checking build system type... x86_64-pc-cygwin
checking host system type... x86_64-pc-mingw32

and over a dozen mingw-related hits before erroring out on libassuan:

         Libassuan v has been configured as follows:

         Revision:   ()
         Platform: x86_64-pc-mingw32

Making all in m4
Making all in src
mkheader.c
usage: mkheader host_os template.h version version_number
make[4]: *** [Makefile:1339: assuan.h] Error 1
make[3]: *** [Makefile:462: all-recursive] Error 1
make[2]: *** [Makefile:394: all] Error 2
make[1]: *** 
[D:/libre/lode/dev/core/external/libassuan/ExternalProject_libassuan.mk:26: 
D:/libre/lode/dev/core/workdir/ExternalProject/libassuan/build] Error 1
make[1]: *** Waiting for unfinished jobs....
make: *** [Makefile:299: build] Error 2

Would be tempting to just uninstall MinGW, but the newcomer needs it for 
other stuff. How can we teach Cygwin to ignore MinGW?

Ilmari