Often this is used to stop people from making any form of judgments about others. But did Christ mean only the sinless can accuse? Not at all. The Lord Jesus is applying Deut 17:7, “The hands of the witnesses shall be first upon him to put him to death, and afterward the hands of all the people. So thou shalt put the evil away from among you.” The sense is this, the person that isn’t guilty of this particular sin and caught the woman in the act, let that person act first.
That’s the stipulation of the law and it prevented people making hasty judgements and pressed upon them the solemn task of also executing the sentence, and this the Jewish leaders were unwilling to do, because then the one who first caught the woman would also have to testify against the man who was strangely absent.