Why doesn't grep using pipe work here?

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'

Your command should be:

find / -name libGL.so.1 2>/dev/null

Find is complaining about permissions on standard error (fd2). In order to eliminate those lines, redirect (>) standard out to the bit bucket (/dev/null).

The "permission denied" lines are going to the stderr (standard error) stream, but you are piping stdout (standard out) through grep.

You can redirect away stderr entirely with

find / -name libGL.so.1 2> /dev/null