We already have the diff_from_contents flag which is used for
--exit-code. We should be able to see where that logic is applied and do
something similar. It looks like it happens in diff_flush(), which makes
sense:

          if (output_format & DIFF_FORMAT_NO_OUTPUT &&
              options->flags.exit_with_status &&
              options->flags.diff_from_contents) {
                  /*
                   * run diff_flush_patch for the exit status. setting
                   * options->file to /dev/null should be safe, because we
                   * aren't supposed to produce any output anyway.
                   */
                  diff_free_file(options);
                  options->file = xfopen("/dev/null", "w");
                  options->close_file = 1;
                  options->color_moved = 0;
                  for (i = 0; i < q->nr; i++) {
                          struct diff_filepair *p = q->queue[i];
                          if (check_pair_status(p))
                                  diff_flush_patch(p, options);
                          if (options->found_changes)
                                  break;
                  }
          }

So here's a naive application of the same technique:

diff --git a/diff.c b/diff.c
index 76291e238c..0fe6eb7443 100644
--- a/diff.c
+++ b/diff.c

@@ -6845,8 +6845,28 @@ void diff_flush(struct diff_options *options)
 			     DIFF_FORMAT_CHECKDIFF)) {
 		for (i = 0; i < q->nr; i++) {
 			struct diff_filepair *p = q->queue[i];
-			if (check_pair_status(p))
-				flush_one_pair(p, options);
+
+			if (!check_pair_status(p))
+				continue;
+
+			if (options->flags.diff_from_contents) {
+				FILE *orig_out = options->file;
+				int orig_changes = options->found_changes;
+				int skip;
+
+				options->file = xfopen("/dev/null", "w");
+				diff_flush_patch(p, options);
+				skip = !options->found_changes;
+
+				fclose(options->file);
+				options->file = orig_out;
+				options->found_changes = orig_changes;
+
+				if (skip)
+					continue;
+			}
+
+			flush_one_pair(p, options);
 		}
 		separator++;
 	}

which works on a trivial example. It affects all of raw, name-only,
name-status, and checkdiff. I know Junio said that --raw should not be
affected, but I'm not sure I agree. Anyway, it should be possible to
split the logic by output type.