Buildroot I would leave to you to figure out.
In your honour, I booted my Raspberry Pi with a debian image to get my facts straight. The word ĺogin'does not appear in the /etc/ directory of that. It does have a login, but nothing asks for that. X starts with no login.
To fix yours, try booting with
as a kernel option on the command line. You will be root. I presume you know your partitions, and you can mount them. My / partition is no. 2, so the command to mount that would be
/sbin/mount -o remount,rw /dev/mmcblk0p2 /
mount the / first, then change the end number to mount the others. Use 'swapon <partition> as above for the swap space.
set a PATH
and hunt around. systemctl can surely shut off logins, or maybe a (HACK Warning!) symlink from /sbin/login to /bin/true would fool it.