Your yogurt cup is almost always PP (Polyproylene) Type 5 to maintain stiffness at large size. In that case the answer is throw it in the garbage, they're going to burn it or send it to China/Africa anyway.

The one that blows my mind is washing aluminum cans (or steel). How do you think they're going to get the plastic coating off the cans and remelt it?

I mean don't recycle a full can, but they have washers for recycled materials too.