It's largely in the ceramic shell of the insulator. There isn't any metal to metal contact, the ceramic is just for that purpose. Surprisingly, the ceramic of the insulator is strong in tension, but poor in shear, which is why they use short porcelain shells and make strings of insulators where one gets the benefits of high resistance, tensile strength, and shear resistance.

(source: aliimg.com)

(source: aliimg.com)
Siemens does indeed gave FRP rods, but they don't have the 12 ton rating that most ceramic string insulators have. The FRP are more suited to distribution than transmission where the tower to tower runs are less than 500' and the conductors no more than say Drake ACSR.
The post insulator in the bottom picture of the answer above is typical of a stand-off used in a substation, it tolerates compression loading only as it's not meant to withstand any shear or suspension loading. It's rare to see a stand-off on a tower, but they occasionally show up on distribution poles as long as they're accompanied by the appropriate shear/suspension appurtenances.