One reason why this shrine has been a controversial entity is that it has militaristic feature, exhibiting weapons in its site ranging from sword to tank. It is like a cross between Smithsonian institution and Arlington National Cemetery.
And the most controversial issue is that A-class war crimes are interred there. However, the trial in which some Japanese military officers are sentenced as A-class war crimes has been so controversial that many intellectuals and politicians have cast doubt on its judicial decision regardless of their nationality. Besides, Japanese culture has a characteristic feature in which even a person who committed crime in his lifetime can be enshrined in the same way as innocent people.
Therefore, most Japanese people are not negative to enshrine A-crass war crimes in Yasukuni Shrine. Rather, they are apprehensive about the diplomatic impact due to politicians' visiting to the shrine, concerning the relationship between neighbor asian nations.
However, China and Korea, in the first place, have educational policy in which Japan's war responsibility has been blamed fiercely for strengthening their national unity. And what is worse is that this situation is favorable to western world because they want to keep asian nations splitting for the economic reason.
Yasukuni Shrine, indeed, is so controversial entity and it has been surrounded by the thoughts and interests of many kinds of societal factions. While it always has been a subject of argument in this 70 years, its reality can not be understood without visiting there. There are military costumed men and military veterans performing military ceremony in memorial days. That behavior has been a cause of troubles because for Chinese and Korean people, that military uniform equals to Natis' it.
A significant problem is that Yasukuni Shrine is a private religious corporation that has its own view of history. If it were a national cemetery, there would not be such a performance by individuals and exhibition of weapons. So there has been an opinion saying that a national cemetery should be founded instead of Yasukuni shrine. Anyway, Yasukuni Shrine is a complicated place in many ways and you will be able to feel it if you go there in some anniversary or memorial day such as august 15, the anniversary of the end of war.