find . -exec grep -l 'string' {} \; -print 2>/dev/null

Question

it lists all files in "." that contain the string "string" but don't show dirs with permission denied.

What would it be the equivalent of that but squeezing xargs in between?

Answer 1

find . -readable | xargs grep -l 'string'

Answer 2

you can just use grep if it has -R option

grep -R -l "string" * 2>/dev/null

Answer 3

find . -type f -print0 | xargs -0 grep -l 'string'

This handles names with blanks (etc) in the file names - and assumes you are using GNU find and xargs.