XQuartz cannot start on macOS Mojave 10.14.5
I guess the original problem was solved by the author by reinstalling the OS, but this seems similar to a problem I was having which seems to be the result of different versions of XQuartz (and maybe MacPorts' x11) getting in each other's way, particularly due to restrictions involving code signing security, possibly due to my not properly uninstalling one of them before reinstalling.
I seem to have fixed my issue by completely uninstalling XQuartz following instructions at the XQuartz Mailing List FAQ. A key seems to be logging out and logging back in again to make whatever magic happens that sets the $DISPLAY environment properly. I did this after uninstalling everything, and then again after installing what I wanted.
I uninstalled both 2.7 and 2.8. Running the commands if either is already uninstalled should not cause any issues beyond a warning that the resource does not exist.
Uninstall (XQuartz 2.8 and later)
To uninstall XQuartz 2.8 and later, execute the following in Terminal:
launchctl unload /Library/LaunchAgents/org.xquartz.startx.plist
sudo launchctl unload /Library/LaunchDaemons/org.xquartz.privileged_startx.plist
sudo rm -rf /opt/X11* /Library/Launch*/org.xquartz.* /Applications/Utilities/XQuartz.app /etc/*paths.d/*XQuartz
sudo pkgutil --forget org.xquartz.pkg

Uninstall (XQuartz 2.7.x and earlier)
To uninstall XQuartz 2.7.x and earlier, execute the following in Terminal:
launchctl unload /Library/LaunchAgents/org.macosforge.xquartz.startx.plist
sudo launchctl unload /Library/LaunchDaemons/org.macosforge.xquartz.privileged_startx.plist
sudo rm -rf /opt/X11* /Library/Launch*/org.macosforge.xquartz.* /Applications/Utilities/XQuartz.app /etc/*paths.d/*XQuartz
sudo pkgutil --forget org.macosforge.xquartz.pkg

At that point (after logging out and logging back in) I only installed the x11 software using MacPorts (via sudo port install xorg) and things seem to be working again (after logging out and logging back in).
I am still trying to figure out why, in one user account, Mojave is VERY slow to launch /Applications/MacPorts/X11.app from the Finder and VERY VERY VERY slow to launch x11 when invoking 'xclock' or 'xterm' from the terminal, while in the other user account, X11.app launches much quicker (while still pretty slow).