Does plugging an extension cord into a GFCI outlet affect the protection?

No, plugging an extension cord into a GFCI outlet doesn’t affect the protection. The GFCI monitors current difference at the outlet, and the extension cord is just a pair of wires. As long as the cord itself doesn’t have a fault, the GFCI will still trip if a device leaks current. Just keep the cord in good shape, don’t bury it under rugs, and avoid daisy-chaining cords.