This seems serious. It is impossible to login unless you do so from a desktop environment, not even with the root user. In the journal I get entries like:
Process 1344 (login) of user 0 dumped core
Seems related to systemd. In fact to the home service:
Stack trace of thread 1344:
#0 0x00007f08672a526c n/a (libc.so.6 + 0x8926c)
#1 0x00007f0867255a08 raise (libc.so.6 + 0x39a08)
#2 0x00007f086723e538 abort (libc.so.6 + 0x22538)
#3 0x00007f0866f8a82c n/a (pam_systemd_home.so + 0x2982c)
#4 0x00007f0866f8ca0f n/a (pam_systemd_home.so + 0x2ba0f)
#5 0x00007f0866f7ea4d n/a (pam_systemd_home.so + 0x1da4d)
#6 0x00007f0866f7ebdb n/a (pam_systemd_home.so + 0x1dbdb)
#7 0x00007f08674154cd pam_end (libpam.so.0 + 0x94cd)
#8 0x00005648b3dcff25 n/a (login + 0x4f25)
#9 0x00007f086723f850 n/a (libc.so.6 + 0x23850)
#10 0x00007f086723f90a __libc_start_main (libc.so.6 + 0x2390a)
#11 0x00005648b3dd0c45 n/a (login + 0x5c45)
ELF object binary architecture: AMD x86-64