You want us to change the type "bin_t" into what?
I assumed that you want to relabel the type and I tried relabelling
#chcon -t xdm_exec_t /usr/sbin/gdm3

 but it didn't work. Still stuck with a black screen. I had to disable the
selinux at boot to login to X.
Now I am at
#ls -Z /usr/sbin/gdm3
system_u:object_r:xdm_exec_t:s0 /usr/sbin/gdm3

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