Per a request in the comments of my previous post, let me post a few more of my notes about Yasukuni Shrine.
First of all, it is an independent religions organization not directly affiliated with the government. Over 2 million soldiers are memorialized in Yasukuni. The votes of these relatives have value, but it isn't since the Koizumi days that the media have started picking it up as a big deal. Koizumi ran for office three times before he was successful. The first two times, visits to Yasukuni were never part of Koizumi's campaign, but starting with the third try against Hashimoto, he promised to visit Yasukuni as Prime Minister to try to take this swing vote from the Hashimoto faction. Some believe that this was key to his winning the fourth election. There appears to be some "logic" in domestic politics for his action. However, I think there is a consensus that it makes no sense from a foreign policy perspective and even the US which has been rather neutral on the issue in the past seems to be concerned. On the other hand, some polls show the Japanese public divided on the issue. The Sankei newspaper is currently the only newspaper supporting Koizumi's visits the Yasukuni Shrine. The Yomiuri, which once supported his visits, now criticizes them. Some people believe that maybe there is some secret plan to use this as a bargaining chip with China in the future. However, most people believe that even if this ends up happening it was not particularly planned by Koizumi.
One expert in Japanese religion at this meeting pointed out that the original Nara Buddhism does not memorialize the dead or believe in heaven. He argued that the religious underpinnings of the necessity of memorializing the war dead didn't make sense under real Japanese Buddhism and that we should stop making such memorials in Japan... that Japan should go back to Nara Buddhism where once you died, you were dead. Full stop. Another person commented that there is a division of state and church under the Japanese constitution and these visits are a violation.
This is reiterating the obvious, but the two main point are the class A war criminals memorialized there and probably the war museum. The war museum tries to argue that the WWII was justified.