The visits Prime Minister Koizumi made to the Yasukuni Shrine, I believe, had nothing to do with approval ratings. He paid respects at the Yasukuni Shrine to pay respects to the people of Japan who fought and lost their lives for the country and to pray for the peace of their souls.
Someone is going to win and someone is going to lose. That's also what happens in almost every movie - someone is going to win and someone is going to lose.

