Try using an Unbuffered sys.stderr

cibuildwheel/docker_container.py

@@ -57,9 +57,6 @@ class DockerContainer:
             ],
             stdin=subprocess.PIPE,
             stdout=subprocess.PIPE,
-            # output the subcommand stderr to our stdout. Avoids ordering
-            # problems between log messages on stderr and stdout
-            stderr=sys.stdout,
         )
 
         assert self.process.stdin and self.process.stdout