I am about to change the light seals of my Nikon FE using a self-adhesive light seal foam with 1.5mm of thickness (which is the thickness I've seen recommended for my model). I also need to change the mirror damper, which in my case is nearly totally gone. Can I use the same light seal foam to replace the mirror damper or should I use a completely different type of material?
Although it's usually not the same thickness as the light seals in the rest of the body, the answer is yes.
I've replaced the seals of a number of cameras, and always used the same material for both the light seals and the mirror dampers.
What you do have to bear in mind is that using felt would be a bad idea, as it's much more dense than the foam light seals and thus won't do much damping. You should also preferably steer clear from thinner foams.
Ideally though, you would use the same thickness foam as what the camera originally had installed.