וגם החיד”א בשם הגדולים לא כתב בגנותו, הגם שלא הללו
But neglects to mention that in that very entry Chida refers to Chayei Yehuda quoting a comment from the Sefer in regard to Gilgul (Chida also refers to Modena in Maagel Tov). At best, he could insist that the maskilim interpolated their own thoughts into the work. As in regard to Megillas Sefer, parallels abound and the accusation would be really foolish as well.
An interesting counter example of cognitive dissonance this time from the maskilic side can be found in Igros Yashar pg. 82 ff. In this case, because Yashar could not accept that his hero would believe something so irrational. He therefore argues with great vehemence that Chayei Yehuda could not have existed (for the really ridiculous reason that "why would he wait to write his memoirs until the end of his life) and - making use of an argument that has become very popular today to dismiss any view of any great Rabbi that doesn't conform to contemporary standards of religiosity - he insists that it must be some mistaken student who believed in Kabbalah who copied it over in the name of his teacher.
(Adelman in his dissertation refers to Yashar's arguments as a "multiplicity of mutually exclusive and self-defeating responses to the problem of Modena's supposed recantation of his views against transmigration. Today it would be argued that Reggio's scholarly accomplishments were in the service of his ideas and beliefs. It was, in fact, Reggio's desire to undermine the Kabbalah which prompted his research into the life and writings of Modena in the first place. When he found information which was contrary to his requirements, such as Azulai's report aobut Modena's recantation, he probed even deeper to explain it away. )
Similarly, A. Geiger conveniently omits the Gilgul story in his biography of Modena. So much for the great "objective critical scholarship" of the 19th century.
Here is Howard Adelman's analysis of Chida's excerpt of Chayei Yehuda in his exhaustive dissertation on Modena pg. 28 ff.:
Azulai wrote that Modena had recorded all that had happened to him during his life, including personal matters. According to Azulai, Modena had also written that at first he did not believe in transmigration of souls, already a well known fact by 1774. Then, according to Azulai's report a neighbor of Modena's gave birth to a son who within a month became very sick. When after six months the infant began to expire, his mother called in Modena to recite biblical verses. While Modena was there, the infant sang hymns, said the "Shema" (Deuteronomy 6: 4), and then died.
From that day on, according to Azulai, Modena believed in transmigration of souls because he had seen that the young child had the soul of an old sage in him. 30
This account was very important for future studies of Modena. It seemingly contradicted all of Modena's anti-kabbalistic writings. The appearance of this story in Azulai's catalogue motivated many subsequent researchers to seek more information about Modena's views on Kabbalah as
well as to find a copy of Hayye Yehudah. Many tendentious views of Modena would be based on Azulai' s account. Most writers, especially those who opposed Kabbalah, considered
it to have been a forgery.31
The story related by Azulai is not in any known manuscript of Hayye Yehuda~, including the autograph copy. However, it still needs explanation. 32 It appears unlikely both that Azulai actually had a copy of Hayye Yehudah in his possession and that he invented the story in its entirely.
Had he desired to discredit Modena on the basis of his autobiography, there was enough incriminating material in it itself, so that there would have been no need to forge material. It is also noteworthy that Azulai did not make use of the great wealth of bibliographic information contained in Hayye Yehudah. Significantly, Azulai wrote that he had "seen" Hayye Yehudah. It is possible that on his short visit to Venice in 1754, when he saw copies of Ari nohem, he also got a brief look at Hayye Yehudah and made quick hostile references to that work in his journal, too. 33
Twenty- f.ive years later, after having read many books and manuscripts with descriptions of similar incidents, including one in Sefer elim by Joseph Solomon Delmedigo,34
who was mentioned regularly by Modena in Ari nohem, and another in Ari nohem itself concerning a man's soul which entered a young girl because he had denied that Simon bar Yohai was the author of the Zohar, 35 Azulai confused some of the details of these stories with Modena. Two additional facts may have contributed to such confusion. At the time that Modena was becoming known as the leading anti-kabbalistic figure, the church had just exposed him as
a newly discovered convert to Catholicism.
Further, Modena himself may have planted the seed for Azulai's claim at the end of Ari nohem: there he wrote to Joseph Hamitz, his former student and a leading kabbalist, to whom the book had been addressed, that he hoped Hamitz would respond to the charges raised against the Kabbalah in Ari nohem, but cautioned Hamitz not to try to refute them in hopes that Modena, as the kabba1ists claimed about Maimonides, too would recant his views against Kabbalah. 36
As opposed to the attitude of Goldschmidt, Shir was able (at least at first) to accept that a great man can have faults and still be considered great (Igrot Shir pg. 71):
מספר חיי יהודה, אשר האיש המסופר ממנו גדול בעיני מאז עד מאד, ועוד גם עתה אחרי כל החסרונות הנודעים לנו ממנו.
However on learning of Modena's heterodox views as expressed in his sharp criticism of Rabbinic Judaism in Kol Sachal, Shir quickly changed his tune (Igrot Shir pg. 208):
לא נבהלתי משמיע קול סכל ושאנת אריה, זה האריה אשר נגלו עתה שניו הטורפות ונראה למחנק נפשות, כי היה מאז חשוד בעינינו, אחרי ידענוהו למבלה זמנו במשך רוב שנותיו לשחק בקוביא, ועם כל ידיעותיו וחמדת לשונו ונועם תוכחתו לרבים בפה ובכתב, לא היה יכול לשחרר את נפשו מתאוה בזויה כזאת. ועתה ננלה לעיני כל כי מרמה היתה כל תוכחתו. צוף על לשונו ולענה בקרב לבו. ותחת אשר קרא לעצמו בונה, סותר יקרא, כי סותר באמת כל התורה . ועד מהרה נתתי לו שם ויד בין איזה חנפים וצבועים אשר לבשתנו נמצאים גם בעמנו[I see Artscroll's Early Achronim has an entry on Modena which I look forward to reading, I suspect their treatment of him was similar to that of R Azariah De Rossi.]
 A reference to Modena's commentary on Ein Yaakov - HaBoneh