Looking at all the propaganda posters during the war, it seems Hirohito was by far the most hated man in America, moreso than even Hitler. The deal with the Emperor doesn't seem to have been something that affected Macarthur's career, either.
I can give a little explanation of why and how the governments on both sides made sure there wasn't a massive adverse reaction, if not really what the reaction was.
Both the Japanese and the Americans expended a significant amount of effort in the post war period to portray the Japanese people and Hirohito in particular as pawns of the Japanese military that were dragged unwillingly into a war. For the Japanese the reasons for this are obvious - they didn't want to be hated and punished for their atrocities, they wanted to do everything they could to distance themselves from it in fact.
For the Americans there were significant advantages too. Ultimately in the post war period the US saw Japan as a potential significant stabilizing influence in Asia, and a powerful ally against the communists. In order to get the US populace to support this they had to try to undo a degree of their war time propaganda casting the Japanese as a whole as evil. As Hirohito and the imperial family was a major sticking point in negotiations, they had to cover them as well in this, as they couldn't really afford to oust the Emperor.
How much is this true however is dubious. Hirohito and the populace and a whole certainly didn't seem opposed to the war early on, and members of the imperial family committed significant war crimes during the war most noticeably Prince Asaka's role in the rape of Nanking. Ultimately however it was expedient for both sides, so it became the prevailing view it certainly helped that Hirohito took steps to surrender at the end of th war, and appeared contrite, and it is certainly true that most of Hirohito's power was symbolic, but I'm not sure it is true to cast them as unwilling.
Related, was anybody mad that we insisted on unconditional surrender then let them keep the emperor? If we had told them up front they'd keep their emperor, peace might have come sooner.
I have a follow up question - how is the Japanese defeat handled in current times? Is it totally glossed over? How is it handled in respect to the national pride that Japanese hold so valuable? How does it compare to how Germans and Italiand handled defeat?
Hirohito had very little real power in fascist Japan. Yes, he went along with the war, but if he had stepped out of line he would have been quickly reigned in. This is in fact what very nearly happened in the two days preceding the Japanese surrender. The anti surrender faction of the military effected a coup that silenced the emperor temporarily while not actually removing him from "power." Source: the excellent book "The Longest 48 Hours"