Besides getting intel64-sandybridge stage3 file, I have also set variables:
CHOST x86_64-pc-linux-gnu CFLAGS -march=corei7-avx -O2 -pipe
I do not think it is a good idea to bother cups/networkmanager/other package developers/maintainers, because that does not appear to be package specific. I would say systemwide instead.
I removed everything and started from scratch, going back one step to intel64-nehalem subarch (with a corresponding CFLAGS change), all illegal instructions have gone like a magic.
So to summarize, I know how to fix it, but have no idea why