what would have happened if the emperor was kicked out after WWII?

[Prince of Chota]

I think it's safe to say that there was very bad blood between the Chinese and Japanese at the end of the war; the sentiment is still felt around China to this day. So it's rather difficult to imagine a situation where Japan would have been swept up in the wave of Maoism that swept the warlords out of mainland China, I doubt that the communists in China could have accomplished it. They had enough trouble getting all of the mainland under the same banner, let alone the massive Japanese population. And having lived in China for a time, I can't say that the Maoist form of communism is the worst government one could be stuck with.
I do think that people today don't understand how unifying a monarchy actually is. It's something I always heard from my grandparents' generation, who remember the war and how powerful the royal family (in our case George VI and Elizabeth Bowes-Lyon) were in maintaining national unity and morale.
We also should decide if we're talking about a general abolition of the Japanese monarchy, or physically removing the imperial family from the country (in which case they'd probably just be living in exile in Europe--maybe Belgium like the Korean Shin de Pyongsans?)
Yes, President Carter didn't do much for the Shah (is Carter little?), but I don't see how Maximilian of Habsburg (or Mexico if you recognize that) is relevant. The Mexican people and their elected government were hardly happy with the idea of a foreign-imposed monarch, even if he was supported by the ethnically-European (Criollo) aristocracy of the country. The scenario is completely different: the monarch in question isn't indigenous (Maximilian wasn't a Tlatoani or Caltzontzin as Hirohito was a Tenno), and the reason for his removal wasn't an invading foreign power (instead, the foreign support that was his powerbase had disappeared). For the sake of fairness, Maximilian wasn't the puppet that Napoleon III had hoped he'd be. But, unfortunately for him, Maximilian wasn't Mexican.
I agree completely with Bones about the issue of State Shinto. Every culture is entitled to its own beliefs, and one could easily make the argument that the concept of the "American Dream" is their own form of state religion. It isn't appropriate to say that Japan isn't a religious nation today, just that Japanese and other Eastern religions do not manifest themselves the same way that the Western religions do. My experience in East Asia is that these are in fact very religiously faithful cultures. However, there isn't the need that Westerners have to maintain ties and identify with one religion alone. Japanese often use Christianity for (western style) weddings, Buddhism for funerals, and Shintoism for the major markers of life (first day of school, birth of children, etc). The attempt by the United States to stomp out State Shintoism made sense at the time, but from some distance appears to conform to a larger trend of cultural misunderstanding and colonialist tendencies.