Oh yeah they exist. There are ceramic ones and I have also seen plastic ones.
I've seen other fun specialized types of screwdrivers in my career:
Screwdrivers with conductive plastic in the handle, to deal with ESD requirements in the spacecraft industry. Alternatively, take a normal plastic screwdriver handle and wrap it in copper tape.
Beryllium screwdrivers (non-ferrous) for use around MRI machine bores thanks to the insane magnetic fields. You also have to wear ceramic hard-toed shoes.
Yes, beryllium is very nasty. You don't ever want to breathe its dust, so don't machine/cut/grind it ever. There are usually warning symbols on things containing it. But it has applications so it gets used.
For example, it is used in spacecraft to save weight over aluminum. When I worked with MRI machines, we used FETs with beryllium oxide ceramic (BeO) backing. BeO is an amazing thermal conductor, electrical insulator (only diamond is better).
It's mostly an inhalation risk. You definitely don't want to be around the manufacture of it without serious PPE, but touching a screwdriver should be fine. Just don't take it to a grinding wheel.
I'd guess anyone working on an MRI machine is wearing gloves anyway for other reasons.
At a company I used to work for we used to get a set of these every time we made a bulk order. But the company was just four people and we made those orders 3 or 4 times a year, so eventually we were basically drowning in very well insulated hand tools.
I've seen other fun specialized types of screwdrivers in my career:
Screwdrivers with conductive plastic in the handle, to deal with ESD requirements in the spacecraft industry. Alternatively, take a normal plastic screwdriver handle and wrap it in copper tape.
Beryllium screwdrivers (non-ferrous) for use around MRI machine bores thanks to the insane magnetic fields. You also have to wear ceramic hard-toed shoes.