It is forbidden to feed bread to a Jew who will not wash his hands. Since doing so would cause him to sin, it is a transgression of lifnei iver lo sitein michshol. If a person who refuses to wash would become angry if he was not fed and if this might cause him to harbor animosity towards religious Jews, there is a concern of chilul Hashem. He might end up proclaiming that religious Jews are rude and have no manners. In such a case, some poskim allow him to be fed one time, with the instruction to wash and recite brochos. If he was fed once, he can no longer claim that religious Jews are nasty. After that, he may not be fed unless he agrees to wash and make a brocha. If there is a chance that feeding him will bring him closer to Torah and mitzvos, it is permissible to feed him even if he does not wash his hands.
ס"ב ס"ק י' ביאורים ומוספים דרשו 7, 10