For some time, Liberal Democratic Party politicians have made no secret of their longing for the "good old days" when Republicans lived in the White House. Besides the typical nostalgia, it is difficult to comprehend Japanese conservatives' preference for the GOP (Grand Old Party as the U.S. Republican Party is known).
Ideologically there is little in common between both groups. American conservatives, even more than liberals, worship individualism. They seek to restrict the power of the state. American conservatism is centered on the individual, Japanese conservatism is communitarian. Government for Americans exists to serve citizens, for Japanese conservatives, subjects are there to serve the state.
The right to bear (fire)arms, vital to many Republicans (and some Democrats) is partly rooted in the belief that a free people must be able to overthrow tyranny.