Does polarity affect hardness?

Hardness is a measure of the resistance of a material to penetration. If the polarity of the polymers change (or if you are using different polymers with different degrees of polarity), the inter-molecular bonding will be different, therefore, the force required to move those polymer molecules around changes. You need to realize that, in order to deform a material plastically (permanent change in shape), you have to rearrange the atoms/molecules making up that object. In order to move those things around, you have to overcome the inter-atomic/inter-molecular forces bind them together.