A mumor l’tayovon (lit., rebel due to temptation) is someone who regularly submits to temptation in violating a specific mitzvah. While the prohibition against gossip mongering does apply with regard to speaking about him (as he is not a heretic), his situation differs drastically from one who occasionally transgresses a given mitzvah but basically is committed to its observance.
As we have learned, the primary prohibition against speaking loshon hora is lo saylaych rachil b’amecha, Do not go as a gossipmonger among your people (Vayikra 19:16). One who embarrasses his fellow Jew transgresses the prohibition lo sonu ish es amiso, A man shall not aggrieve his fellow (Vayikra 25:17).Our Sages interpret the term amecha, your people, in the first prohibition as excluding only a mumor l’hachis, (lit., rebel whose intent is to spite), one whose lack of regard for a given prohibition causes him to regularly transgress it. However, the term, amiso, his fellow, in the second prohibition, excludes even the mumor l’tayovon. Thus, it is forbidden to speak loshon hora about a mumor l’tayovon but it is permissible to exert social pressure on him in order to induce him to mend his sinful way.
It is permissible to publicize that a Jew regularly violates a particular halachah if it is clear that he is aware of the halachah and has chosen to ignore it, and it stands to reason that publicizing his behavior will induce him to change. This applies even if he transgresses the law out of temptation. However, one must be certain that all the conditions of toeles, constructive speech, including purity of intent and lack on an alternative, apply.
