I would be great if someone would supply the relevant verses.
From what I recall in Jesus' teaching about not judging other, I also recall he mention somewhere about not persecuting others. These 2 teachings must be related; they probably are, but I don't remember. Judging others can sometimes lead to persecution, so I am more concern with this than to simple criticism.
Past history have showed that Christians have failed in heeding this, ie of not persecuting others. When Christianity was in infancy, it was the one being persecuted, but once they wield some powers, some have completely ignored Jesus' statement of not persecuting others.