“The existence of sheidim is not a matter of halachic opinion, they either exist or they do not.”
I would say you got that backwards. If the gedolim -especially rishonim- decide that something exists, even if it hadn’t before, it will from then on exist. It’s the Torah that decides reality not reality that decides the Torah.
“And Rambam was the greatest gedol of the last thousand years.”
I’m not even sure what that means. Standing on the streets on Manhattan are you able to see whether the Empire State building or the World Trade Center (z”l) is bigger? How are you able to determine that the Rambam was the greatest gadol?
In addition the sefer Shomrei Emunim HaKadmon (a Rishon) says that the Rambam was chozer on his more “esoteric” ideas near the end of his life, since he hadn’t learned kabballah until after he had written his sefarim.
The mekubalim do many things to keep sheidim and mazikim away such as shaking their tzitzis after looking at the moon during kiddush levanah. Its likely then, that the Rambam did this as well.
In addition if you are Ashkenaz like me, you don’t pasken like the Rambam but rather the ReMa which clearly state that there are sheidim.
This is similar to the story with man who came to the Chazon Ish for a beracha for a surgery in chutz la’aretz he was going to get for some ailment. The Chazon Ish told him that he sholdn’t go to chutz la’aretz and as long as he stays in E”Y he will be fine. When questioned about it the Chazon Ish said that the Beis Yosef was the posek in E”Y and he held that that particular ailment was not a mum in an animal which means that the animal wouldn’t die from it while the ReMa -who was the posek of chutz la’aretz- held that it was. So by staying in E”Y he kept himself under the auspices of the B”Y and was able to live for many more years.