I don’t remember anyone “lauding” Abe as anything when he first became PM. He’s long been associated with the conservative wing of the LDP (as was his grandfather) and he made his name banging the anti-North Korea drum as chief cabinet secretary under Koizumi (something that kind of bit him in the ass the first time he was in power).
He may be prime minister, but I don’t take that as that great of an endorsement. He did a lot during the period between becoming party president and the election to emphasize his economic plans and not his more controversial views, though to be honest the DPJ had failed so miserably that there was no way the LDP could have lost. I don’t think he’s even all that popular within the party. It came as a bit of a surprise that he was elected party president last year, since it came almost entirely on the backs of the Diet party members. He’d only gotten the votes of 29% of the local party leadership, IIRC.
The Yomiuri Shimbun had an interesting article (in English) showing some of the behind the scenes stuff for Abe’s visit. I recommend it.
As for politicians in general visiting Yasukuni, I think that’s a more complicated issue. I wouldn’t necessarily assume that every LDP Diet member who makes the “pilgrimage” is in lockstep with Abe’s historical views and the same goes for the average citizen who supports such visits. Right now contemporary anti-Chinese sentiment is more relevant than views on historical issues. There’d likely be less support for such visits if not for recent clashes with China over the East China Sea.
Kyodo News (a major Japanese wire service) released the results of a public opinion poll they took on the visit. 43.2% approved and 47.1% disapproved of prime ministerial visits and 69.8% thought that diplomatic relations should be taken into consideration in such visits.
There was also a Asahi Shimbun poll on the war, though it’s behind a pay wall so I can only find a few excerpts. Asked the question “Do you think the Pacific War was a war of aggression?”, 33% of those in their 20s answered “no”, compared to 24-28% in other age brackets. I think that a lot of Japanese consider the war with China to be a separate conflict from the “Pacific War”, though, so that should be kept in mind.
The fullest survey I was able to find on Japanese perceptions of the war was from 2005. In that one, 34.2% felt “both the war with China and the war with the US (including the UK, Netherlands, and other Allies) were wars of aggression”, 33.9% felt “the war with China was a war of aggression, but the war with the US was not.”, 10.1% felt “neither were wars of aggression”, and 20.7% didn’t answer. Perhaps the most interesting result was that when asked “Which of the following do you feel bear great “war responsibility”? Select any number”, only 5% selected “the general public” (and only 19.3% chose the Emperor).