How can I avoid the "grep: Argument list too long" error?

You can use the -n option of xargs to limit the number of arguments.

find . -name "*" | xargs -n 20 grep 'state-icons'

But a better solution is to use -type f instead of -name "*" in order to limit the list to ordinary files, avoiding the error message for each folder.

Note that it does not work for files with whitespace in their names.