The correct answer is: we hate to waste food, so we put all our kitchen scraps in the compost pile.
Indeed, you use semicolons when you have two independent clauses, i.e. clauses that have independent ideas that can stand on their own. This applies to both of the clauses. Here, we have the first clause about hating food waste which definitely stands on its own. The second clause refers to the act of putting kitchen scraps in the compost pile. It is an independent idea, it is not connected with food waste since scraps that are put in the compost pile are no longer food.