Talking in the theoretical as opposed to the case at hand, if someone passing himself off as a talmid chacham and צדיק would be living a double life, passing himself off for years to non Jews as a Roman Catholic, being mizaneh with hundreds of non Jews בשאט נפש, mechalel shabbos, treif restaurants etc. and if theoretically at some point it became well known, at some point wouldn’t it rise beyond the level of בעל עבירה and be מן החנפים and אינו עושה מעשה עמך so that it would be מותר to speak about and denigrate that person even if we were to assume that there is no תועלת (other than מפרסמין החנפין)? I know the ח״ח כלל ד׳ in באר מים חיים ל״ב and also in כלל ז וי׳ touches on this. Perhaps someone well versed in these halachos can comment. Again talking in the theoretical.
From looking into some of the sources the inyan is not so clear, but it would appear that if one is known to be repeatedly engaged in an issur that is well known such as arayos it is mutar to speak lashon hara regarding those aveiros though not regarding other areas of his life that do not involve aveiros. However, the lashon hara must be litoeles, which can include dissuading others from following his path as well as shaming him so he is motivated to do teshuva. See Chelkas Binyamin in כלל ד who is puzzled as to why the heter is limited as opposed to a מומר.
There is a seperate din of exposing one who pretends to be a צדיק but engages in aveiros so that others should not learn from him which may or may not apply in a case such as this. If indeed one was living a complete lifestyle that involved wanton arayos, chilul shabbos, treif, and claiming to be a catholic it is not clear if he is still called a מומר לתיאבן who is still considered עמיתך or if he is no longer considered עמיתך in which case it would be מותר even without toeles though not necessarily advisable.