One solution is to login directly as the user as which you want to run thos X11 programs.
One more workaround is there.Here you can login as a different user. Thereafter run the below command
xauth list | grep "`hostname`/"| grep `echo $DISPLAY | cut -f2 -d: | cut -f1 -d.`
Copy the output. Then switch to second user and run xauth add as this output as an argument as below
xauth add training/unix:13 MIT-MAGIC-COOKIE-1 57f03bee06be924299b0bedde6499bd1
Now run any X11 programs.