Sendmail chdir(/clientmqueue) permission denied
Sendmail-8.12+ installation: file permissions
Sendmail-8.12+ binary should be installed as set GROUP id.
(/usr/sbin/sendmail.sendmail in your case)
It is described in SECURITY file in sendmail(.org) distribution:
-r-xr-sr-x root smmsp ... /PATH/TO/sendmail
drwxrwx--- smmsp smmsp ... /var/spool/clientmqueue
There's also an SELINUX boolean policy called httpd_can_sendmail.... I'm pretty sure this has to be set to true also.