Finally, I manage to keep my Ethernet connection from going down after a minute. I do not know why, maybe because I enterd ifconfig_re0="inet 192.168.1.107 netmask 255.255.255.0" instead of ifconfig_re0="DHCP" in rc.conf.
Unfortunately, until the reboot. No means prevent a non-working WiFi from being loaded and turned on instead of Ethernet. Here is the network part from my rc.conf:
if_wlan_load="NO"
if_re_load="YES"
if_re_name="/boot/modules/if_re.ko"
ifconfig_wlan0="NOAUTO"
# wlans_iwlwifi0="wlan0"
# create_args_wlan0="down country LT"
# ifconfig_wlan0="up scan WPA DHCP"
# ifconfig_wlan0_ipv6="inet6 accept_rtadv"
ifconfig_re0_ipv6="inet6 accept_rtadv"
ifconfig_re0="inet 192.168.1.107 netmask 255.255.255.0"
defaultrouter="192.168.1.1"
I have thoroughly read the network and advanced networking chapters in the handbook, ifconfig, iwlwifi, re, dhclient, loader.conf and rc.conf manuals, but I have not found an explanation of what prevents loading RTL8125, why WiFi is preferred to Ethernet, and why my directives to disable a non-working WiFi are ignored and even overwritten.
Interestingly, my instructions in rc.conf are executed on boot, but cancelled and rc.conf is overwritten later, after Xorg has been loaded, with no explanation in the syslog.