grep -v or grep --invert-match doesn't work on Big Sur
grep is not broken per-se in macOS Big Sur.
The output you are seeing is stderr output from the ducommand and it is a separate stream from stdout that is being being piped to grep.
Use du -h -d 1 2>/dev/null instead, or use du -h -d 1 2>&1 | grep -v 'not permitted', however, I'd use the former instead in this particular use case.
Have a look at Standard streams as a reference on standard input (stdin), standard output (stdout) and standard error (stderr).