How do I prevent a capacitive touch from registering?
Generally materials will have a dielectric constant in the range of 2-3 (air is 1.0) so a fabric of (say) polyester behaves similarly to an air gap of about 1/3 the thickness (a bit more because of the air in the polyester fabric). So if your device will not register an air gap of say 1mm then a 3mm thick fabric will probably work. 

I don't believe that there is anything magic that will allow the material to be thinner than the minimum air gap for sure, and probably several times that.