Construction differences are more pronounced and more important than material differences. All tires are belted, whether it is bias belted or radial belted. The belts are what's under the rubber that determine all the ride and load characteristics.

Materials for radials can be steel, polyester, fiberglass, Twaron, Kevlar, or combinations of these.

Mixing of bias and radial on a car does create different feel because of the radials tendency to be more compliant while the bias ply tends to be more rigid. This can create conflicting feel and reaction that can make the car feel different. Mixing them won't automatically make your car burst into flames and if you understand the handling differences, you can adjust driving technique. However, for most of us, its easier to simply put compatible tires on all four corners.

I don't doubt that the old Polyglas tires, the BFG belted TA and radial TA , Pontiac's radial tuned suspension of the mid 70s, and all the warnings of mixing tire construction when we were younger has created some fuzzy memories for some of us.