The Rambam holds a special place in the Yeshiva world and is the centerpiece of much of Yeshivish Torah. More ink has been spilled trying to explain difficult psakim of the Rambam then on any other subject and the Rambam is very much the focus of the shiur klali given by the Roshei Yeshivas. The Briskers in fact take this even further and are machmir on many/most issues to follow the Rambam even when he is a minority opinion.
And yet, there is no question that hashkafically the Rambam would completely disagree with current Charedi hashkafa. Here are some examples:
1. The Rambam is vehemently opposed to the practice of people taking money to learn (e.g. Kollel), he writes this both in the Perush Hamishnayos on Avos (4:5), where he has a very lengthy screed against this practice, and in the Mishna Torah (Hilchos Talmud Torah 3:10)
אמרו חכמים, כל הנהנה מדברי תורה, נטל חייו מן העולם. ועוד ציוו ואמרו, לא תעשם עטרה להתגדל בהם, ולא קורדום לחפור בהם. ועוד ציוו ואמרו, אהוב את המלאכה, ושנוא את הרבנות. וכל תורה שאין עימה מלאכה, סופה בטילה; וסוף אדם זה, שיהא מלסטס את הברייות.
2. The Rambam learned philosophy and included it in his sefarim. Believe it or not, the Rambam writes in the שמונה פרקים (his introduction to Avos) that his sources are chazal, the geonim, and the philosophers (meaning Aristotle). Of course, today philosopy and in fact, any secular studies are absolutely verboten in the Charedi world
3. The Rambam was a doctor who had extensive secular knowledge and practiced as a doctor
4. The Rambam not only knew the vernacular (Arabic) but he wrote Sefarim (פירוש המשניות) in it
5. The Rambam understands that many things that are written in Chumash and Chazal never happened but are allegories (for example the story with the 3 angels at the beginning of וירא) or dreams. In addition the Rambam holds that chazal can make a mistake in science.
6. The Rambam did not believe in magic even though the Gemara has many stories regarding magic, see yesterday's post
Did the Tannaim and Amoraim believe in magic?
7. The Rambam did not believe in absolute Hashgacha (see my post
Hashgocha Pratis, what does it really mean?), rather he believed that most people had no hashgacha. Of course, the Charedi world today believes that everything is a gezera from heaven and a leaf doesn't fall without it being decreed in heaven.
Does the Yeshiva world not know this? Do they just ignore this?