The mesa DRI drivers (and possibly other binary packages I haven't
tested)  appear to violate the i386 baseline by using SSE2
unconditionally, even if the host CPU doesn't support it (tested on a
Pentium III), which results in even the simplest programs like glxinfo
or glxgears crashing with SIGILL.

The solution is simple: rebuild the package with the meson option
"sse2" set to false, to follow the Debian baseline.