B"H, I believe I've discovered who is being referred to here.
First of all, as I mentioned in the comments, this quote is not from the Chida but from R' Menachem Mendel Krengel, who published a revised version of Ben-Yaakov's edition of Shem Hagedolim. Since the B"Y Edition, it has become customary for just about every new edition of Shem Hagedolim to have new sections and/or footnotes added to the original text (source). R' Krengel added info mostly about Polish rabbis and books that the Chida wasn't aware of or had come out after his death, but he also added a number of footnotes which he titled "Hagahot Menachem Tzion". The OP's quote is from one of those footnotes.
The "Maskilim" here, I believe, is a reference to a kuntress called "Givat Yerushalayim: Chakirah Al HaTalmud HaYerushalmi, Mekoro, Inyano U'Zmano" by R' Dr. Yonah Wiesner, and by extension, the other maskilim who agreed with him, or partially agreed with him. The kuntress came out in 1871, a little over 30 years before R' Krengel came out with his Shem Hagedolim. In the kuntress, R' Wiesner sets out to prove that not only was the Yerushalmi not written before the Bavli, but it was written either by a Karaite or a Karaite-sympathizer, building over an old tosefta and was intended as a work of satire, mocking the rabbis and strengthening the Karaite positions. I'll bring some examples:
Pg. 7-8:
"ואגב אורחא לא אכחד שמה שנמצא בירושלמי (שם פ"ב ה"ד): "א"ר חייא חובא אנא מן יומי לא כוונית אלא חד זמן בעי מכוונה והרהרית בלבי ואמרית מאן עליל קומי מלכא קדמי ארקבסה או ריש גלותא, שמואל אמר אנא מנית אפרוחיא, ר' בון בר חייא אמר אנא מנית דימוסיא, א"ר מתניה אנא מחזזק טיבו לראשי דכד הוה מטי מודים הוא כרע מגמריה", לדעתי שקר גמור הוא, יען אלו המורים אנשי השם ובראשם ר' חייא רבא בודאי התפללו בכונה כיאות לאנשים צדיקים יראי ה', ואם לפעמים באשר יציר אדמה היו, לא עלתה בידם לטהר את מחשבתם כראוי, בודאי היו חסים על כבוד קונם ולא היו מתפארים בכך כאחד הריקים. ומה לו לר' חייא רבא שהיה שרוי בא"י לחשוב מחשבות על ריש גלותא ועל אלקפתא שבבבל או בפרס מה לו ולהם? אלא ודאי כל הדברים האלו בדוים הם, ואולי חכם או מעתיק מבני מקרא כתבם להתלוץ על גדולי הרבנים, כאשר נראה להלן ששלטו הקראים בתלמוד הירושלמי ועשו בו כרצונם."
"and by the way, I won't deny that what's written in the Yerushalmi (there 2:4): "Said Rabbi Chiya [not too sure how to translate this line, but he's saying that during prayer, he would think about the king or about the reish galuta], Shmuel said: "I would count chicks", R' Bon bar Chiyah said: "I would count [dimosiya], said R' Matanyah I would fasten [tivu] to my head [something about bowing during modim]", In my understanding this is a complete lie, for all of these teachers were great people and above them R' Chiya Rabah who surely prayed with concetration, as befits righteous men, Hashem-fearers, and if they would sometimes be as a creation of the earth, and they didn't manage to purify their thoughts as needed, surely they would grace the honor of their Lord and wouldn't boast like one of the simpletons. And what did R' Chiya, who lived in Eretz Yisrael, have to do with thinking about the reish galuta and the Alkafta in Bavel or Persia, what did he have to do with them? From this we see that all of these things were invented, and perhaps a sage or a scribe from the Bnei Mikra [early name of the Karaites] wrote these things to mock the rabbinical giants, as we shall see later on how the Karaites controlled the Talmud Yerushalmi and did with it as they pleased."
Pg. 13:
"בירושלמי (שבת פ"א ה"ד): איתא: תנא ר' יהושע אונייא, תלמידי ב"ש עמדו להן מלמטה והיו הורגין בתלמידי בית הלל, תני ששה מהן עלו והשאר עמדו עליהן בחרבות וברמחים". על הדבר הזה ישתומם כל נבון, מי שמע כאלה שיהיו חכמי ישראל הורגין זה את זה, ובקנאתם קנאת סופרים ימהרו לשפוך דם נקי ח"ו, ואדרבא אמרו בתוספתא (יבמות י"ד ע"ב) אע"פ שנחלקו ב"ש וב"ה בצרות וכו' לא נמנעו ב"ש לישא נשים מב"ה ולא ב"ה מב"ש, ללמדך שחיבה וריעות נוהגים זה בזה לקיים מה שנאמר האמת והשלום אהבו. אלא ודאי נשתקע הדבר ולא נאמר והמחבר הירושלמי בדא את הסיפור המכוער מלבו. – וכאן המקום להעיר איך הקראים הסתייעו בזה המאמר של הירושלמי להוכיח בכל דור ודור עד שאיש את רעהו הרגו בחרב. והחכם הקראי סלמון בן ירוחם (885-960) לא נתעצל לכתת את רגליו מא"י לבבל ובידו תלמוד ירושלמי סדר מועד עם פירוש יעקב בן אפרים (זה המפרש לא נודע שמו במחנה הרבנים בלי ספק גם הוא קראי היה והם החולמים הם הפותרים) לדבר משפטים עם רס"ג, שהחליט, שחכמי ישראל אף שחולקים זה עם זה בהלכה, בכל זאת אהבה ואחוה היתה ביניהם (עיי' רש"פ לקוטי קדמוניות, נספחים צד י"ד). וזה דרכם של הקראים להמציא ספרים מזויפים על שם חכמים הראשונים..."
"In the Yerushalmi (Shabbat 1:4) it is brought: R' Yehoshua Oniyah taught, The students of Beit ShamMai stood beneath them and would kill by the students of Beit Hillel, we learned that six of them rose and the rest stood over them with swords and spears". On this any intelligent person will wonder at, who ever heard that the sages of Yisrael would kill one another, and in their zeal of scribes would rush to spill clean blood Cha"V, but the opposite, in the tosefta (Yevamot 14b) Beit Shammai did not refrain from marrying women from Beit Hillel, nor did Beit Hillel refrain from marrying women from Beit Shammai. This serves to teach you that they practiced affection and camaraderie between them, to fulfill that which is stated: "Love truth and peace". Surely, this was hidden and not stated and the author of the Yerushalmi invented this ugly story. - And here it is the place to state that the Karaites were assisted by this story of the Yerushalmi to prove in every generation that it was until a man slew his friend by the sword. And the Karaite scholar Salmon ben Yerucham (885-960) was not lazy and went from Eretz Yisrael to Bavel and in his hand the Talmud Yerushalmi, Seder Mo'ed with the commentary of Yaakov ben Efraim (this commentator was not known by the encampment of the rabbis, without a doubt he was also a Karaite, and they who dream are those who solve), to argue with RaSa"G, who decided, that though the sages of Yisrael disagree with one another in halacha, there was still love and friendship among them (see RS"P Likutei Kadmoniyot, appendix pg. 14). And that is the way of the Karaites to invent forged books upon the name of the early sages..."
Pg. 52:
"...לכן שפטתי משפט צדק שהתלמוד ירושלמי חובר בין אלף ע"ב, לאלף ר"י דהיינו בין 760-900 למספר הרגיל."
"...therefore I judged justly that the Talmud Yerushalmi was written between the elef ayin-bet, and the elef reish-yud, meaning 760-900 to the regular [secular] count."
The year 760 is right around the time of the rise of Anan ben David, the father of the Karaite movement.
And there are many, many more examples throughout the kuntress. He deals with chronological problems, with evidence for the Yerushalmi being older than the Bavli, several "mini-issues" such as R' Elazar ben Hyrcanus and so forth. Interestingly, he makes it clear that his intention is not to simply put down the Yerushalmi, but that he wanted to lift up and empower the Bavli (the more liberal maskilim at the time mocked all rabbinical texts, after all).
The publisher wrote in the beginning that he decided to print this text because he thought that R' Wiesner made many good points, though he didn't agree with all of them. Perhaps for this reason, he attached at the end refutations of several of the points. He also wrote that Avraham Geiger and Aharon Jellinek had seen the work and had been very impressed.
Therefore, I would include in the group of maskilim also Geiger and Jellinek, two of the most noted maskilim of the 19th century.
I would also add to the list Michael Levi Rodkinson, a maskil and the first person to translate the Talmud into English, who wrote in his book "The History of the Talmud", vol I, pg. 157-158:
"As the Samaritans have forged and falsified the Pentateuch...so also did the Karaites forge and falsify the Talmud...Jerusalem Talmud...And they did not conceive that Sahl himself has forged the manuscript of the Talmud by writing in this statement [the one about B"H and B"S killing each other]..."