Ok, I think I've got something, finally

root can log in
catonano cannot

Here:

New session c5 of user catonano.
/gnu/store/r4rfxxi8k4gql53vfcr3ns9l2mksd3m2-xauth-1.0.10/bin/xauth:  error
in locking authority file /home/catonano/.Xauthority
error in finalization thread: Successo
/home/catonano/.bash_profile: riga 5:
/home/catonano/guix/doc:/run/current-system/profile/share/info:/home/catonano/.guix-profile/share/info:/run/current-system/profile/share/info:
File o directory non esistente
declare -x BASH_LOADABLES_PATH="/run/current-system/profile/lib/bash"
declare -x DBUS_FATAL_WARNINGS="0"
declare -x
DICPATH="/home/catonano/.guix-profile/share/hunspell:/run/current-system/profile/share/hunspell"
declare -x DISPLAY=":0.0"
declare -x
GIO_EXTRA_MODULES="/home/catonano/.guix-profile/lib/gio/modules:/run/current-system/profile/lib/gio/modules"
declare -x GIT_SSL_CAINFO="/etc/ssl/certs/ca-certificates.crt"
declare -x GST_PLUGIN_PATH="/home/catonano/.guix-profile/lib/gstreamer-1.0"
declare -x
GST_PLUGIN_SYSTEM_PATH="/home/catonano/.guix-profile/lib/gstreamer-1.0:/run/current-system/profile/lib/gstreamer-1.0"
declare -x GTK_DATA_PREFIX="/run/current-system/profile"
declare -x
GUILE_LOAD_COMPILED_PATH="/home/catonano/.guix-profile/lib/guile/2.0/site-ccache:/home/catonano/.guix-profile/share/guile/site/2.0:/run/current-system/profile/lib/guile/2.2/site-ccache:/run/current-system/profile/share/guile/site/2.2"
declare -x
GUILE_LOAD_PATH="/home/catonano/.guix-profile/share/guile/site/2.0:/run/current-system/profile/share/guile/site/2.2"
declare -x GUIX_GTK2_PATH="/home/catonano/.guix-profile/lib/gtk-2.0"
declare -x GUIX_GTK3_PATH="/run/current-system/profile/lib/gtk-3.0"
declare -x GUIX_LOCPATH="/run/current-system/locale"
declare -x GUIX_PACKAGE_PATH="/home/catonano/projects/local_packages"
declare -x HOME="/home/catonano"
declare -x
INFOPATH="/run/current-system/profile/share/info:/home/catonano/.guix-profile/share/info:/run/current-system/profile/share/info"
declare -x LANG="it_IT.utf8"
declare -x
LIBRARY_PATH="/home/catonano/.guix-profile/lib:/home/catonano/.guix-profile/lib64"
declare -x LINUX_MODULE_DIRECTORY="/run/booted-system/kernel/lib/modules"
declare -x LOGNAME="catonano"
declare -x MAIL="/var/mail/catonano"
declare -x
MANPATH="/run/current-system/profile/share/man:/home/catonano/.guix-profile/share/man:/run/current-system/profile/share/man"
declare -x
NM_VPN_PLUGIN_DIR="/gnu/store/7m12paa3z0y2wl5ya82wqydkw67xj40l-network-manager-vpn-plugins/lib/NetworkManager/VPN"
declare -x OLDPWD
declare -x
PATH="/home/catonano/.guix-profile/bin:/home/catonano/.guix-profile/sbin:/home/catonano/.guix-profile/bin:/run/setuid-programs:/run/current-system/profile/bin:/run/current-system/profile/sbin"
declare -x PWD="/home/catonano"
declare -x
PYTHONPATH="/home/catonano/.guix-profile/lib/python3.5/site-packages"
declare -x QMAKEPATH="/home/catonano/.guix-profile/"
declare -x
SHELL="/gnu/store/ars9lm9jk9hgdifg0gqvf1jrvz5mdg1j-bash-4.4.12/bin/bash"
declare -x SHLVL="1"
declare -x SSL_CERT_DIR="/etc/ssl/certs"
declare -x SSL_CERT_FILE="/etc/ssl/certs/ca-certificates.crt"
declare -x
TZDIR="/gnu/store/bzj472nmnnj5hcfd5yvfiqip1wzw84p9-tzdata-2017b/share/zoneinfo"
declare -x USER="catonano"
declare -x XAUTHORITY="/home/catonano/.Xauthority"
declare -x
XCURSOR_PATH="/home/catonano/.icons:/home/catonano/.guix-profile/share/icons:/run/current-system/profile/share/icons"
declare -x
XDG_CONFIG_DIRS="/home/catonano/.guix-profile/etc/xdg:/run/current-system/profile/etc/xdg"
declare -x
XDG_DATA_DIRS="/run/current-system/profile/share:/home/catonano/.guix-profile/share:/run/current-system/profile/share"
declare -x XDG_RUNTIME_DIR="/run/user/1000"
declare -x XDG_SEAT="seat0"
declare -x XDG_SESSION_ID="c5"
declare -x XDG_VTNR="7"
declare -x X_XFCE4_LIB_DIRS="/run/current-system/profile/lib/xfce4"
No protocol specified

** (process:1256): WARNING **: Could not make bus activated clients aware
of XDG_CURRENT_DESKTOP=GNOME environment variable: Could not connect:
Connection refused
No protocol specified

(gnome-session-check-accelerated:1268): Gtk-WARNING **: cannot open
display: :0.0
No protocol specified

(gnome-session-check-accelerated:1269): Gtk-WARNING **: cannot open
display: :0.0
gnome-session-binary[1256]: WARNING: software acceleration check failed:
Processo figlio uscito con codice 1

** (gnome-session-failed:1270): WARNING **: Cannot open display:
(II) Server terminated successfully (0). Closing log file.
Removed session c5.
Respawning xorg-server.