The program you execute will run under the root user id and will generally have no authority to access your X display. KDE su gets around this by adding an authentication cookie for your display to a temporary .Xauthority file. After the command exits, this file is removed.

If you don't use X cookies, you are on your own. KDE su will detect this and will not add a cookie but you will have to make sure that root is allowed to access to your display.