That's nothing to do with grep - it's because the pipe | redirects the standard output stream stdout whereas the Permission denied messages are in the standard error stream stderr. You could achieve the result you want by combining the streams using 2>&1 (redirect the stream whose file descriptor is 2 to the stream whose file descriptor is 1) so that stderr as well as stdout gets piped to the input of the grep command
find / -name libGL.so.1 2>&1 | grep -v 'denied'
but it would be more usual to simply discard stderr altogether by redirecting it to /dev/null
find / -name libGL.so.1 2>/dev/null
Using |& instead of 2>&1 |
If you take a look at the Bash man page you'll likely notice this blurb:
If |& is used, the standard error of command is connected to command2's standard input through the pipe; it is shorthand for 2>&1 |.
So you can also use this construct as well if you want to join STDERR and STDOUT:
find / -name libGL.so.1 |& grep -v 'denied'