One thing a lot of people have not mentioned is that Asians value moderation and the current GOP is anything but moderate. That was certainly not the case a few decades ago. Even looking at Reagan, he said conservative things in a moderate way. On the other hand the Democrats are a moderate party. Of course Asian Americans will vote for that party.
Other things matter too, such as the anti-intellectualism of Bush which was followed up by the immigration debate which made the GOP look like the white party. And Palin talking about the real America....all the talk show hosts and Fox news heads blabbering about how bad white people have it these days. Oreilly talking about the end of the white establishment in 2012...I could just go on forever. It can be argued that in the 1980s blacks may have felt targeted by the GOP but Asians certainly did not. Now with the moaning about white America amongst conservatives, they most certainly are.
Something else -- Sarah Palin became one of the exemplars of the Republican Party. (1) Her mangled English might appeal to the semi-literate who use language something like she does. (2)Add to that, she made speeches in which she praised the "real" America of small-town and rural America that hasn't been the majority of America for almost a century. (3)Asian-Americans are very bourgeois.
(1) After the 2008 election many thought that she would be a likely candidate for President. I was following the polls on how she projected to do against Barack Obama, and I noticed something remarkable: that although she did no worse than other candidates in states with comparatively few people of foreign origin, she did catastrophically badly in states with large numbers of foreign-born people -- which I use as a proxy for people whose first language is not English. (To be sure, there are people in the US who are native to the US and whose first language is not English, and there are people in the US who immigrated from elsewhere whose first language is English). Others similarly right-wing (such as Mike Huckabee) had no such problem. One may disagree with him, but one fully understands his impeccable English.
If there is a basic rule in talking with anyone whose first language is not English, it is to stay close to the formal register taught in phrase books and basic English texts -- whether the first language is German -- or Korean. How proficient the person is in English matters little; the non-native speaker must process what an English speaker says into thought patterns structured in a different grammar and vocabulary. With slang and mangled diction one must make two translations -- one to formal English and then to the early linguistic heritage of the speaker, which is far more difficult. Sarah Palin is not someone whose diction and word choice I would want to introduce as English speech.
I notice that she went to college in Hawaii... and found it miserable. Maybe there are so many people there whose native languages are Spanish, Portuguese, Tagalog, Chinese, or Korean. (In case you wonder about Japanese -- mass Japanese immigration to the US ended before World War II, and Japanese-Americans are safely assumed to be Anglophone).
(2) Urban America, except for parts of the South, contains the majority of the ethnic and non-Christian religious minorities. Rural America is far more conformist... and conforming to a culture in which one is not raised is difficult. Sarah Palin insulted people not of her culture by castigating Americans outside her conception of "Real America".
(3) This may apply to Sarah Palin more than to other Republicans -- Asian-Americans are very bourgeois in their attitudes toward education and family life. I can't speak for Asian-Americans, but I saw the spectacle in the 2008 Republican National Convention in which one of Sarah's unmarried daughters came in with a baby (OK, that can happen) -- but so did the unmarried young man who fathered the child. Bourgeois types would find the appearance of an unmarried woman with a child in a high-profile public event bad enough, but the unmarried seed-supplier as well? What happens in Hollywood and gets accepted because the person involved is a celebrity who earns millions is very different from what one accepts in the Real World.
A Party that vilifies education will offend educated people even if those people are conservative in lifestyle.