I was reading a book about Lyndon Johnson and it talked about how one of his achievements as majority leader of the senate was getting Hawai'i statehood. The book then went on to mention that "Most politicians conceded that Hawai'i would vote Republican, and Alaska Democratic", in reference to the balance of the electoral college. I haven't read elsewhere that Hawai'i was expected to go red, but I have definitely heard elsewhere that Alaska was expected to be a blue state. For instance, in this video showing some of NBC's 1960 election coverage, the reporter from Nixon's head quarters says "He has said he would not concede any state, not even Alaska, which is generally put in the Kennedy Column, nor would he claim such a state as Maine or Vermont which is generally given to the Republicans".
Although the political landscape was different back then, the prediction has been consistently wrong since both states entered the union. In the presidential election, Alaska has only voted for the Democratic president in LBJ's landslide victory in 1964, and Hawai'i has only voted Republican as part of Nixon's 1972 landslide victory, and in Reagan's 1984 landslide win.
I do know that labor was a huge force in Hawai'i at the time, with the plantation unions and the longshoremen being a strong force in the state (as the previously mentioned book says), but I would imagine the pundits factored that in when making their predictions. So what happened?
Keep in mind that statehood for Alaska and Hawaii took place before American political parties assumed their modern stances. In 1960, the Republican Party was predominantly the party of the North and progressivism. It had more in common with the Republican Party of Abraham Lincoln than of Ronald Reagan (at least, as we see Reagan today). The Democratic Party was generally the conservative party, with roots in the "solid South."
But even in 1960, that was changing. The Democratic Party, as far back as the 19th century, always had two wings: the conservative Southern wing and the more progressive Northern, urban one. FDR managed to hold those two wings together, but they really split in 1948 with the creation of the "Dixiecrats" who ran as a third party in that year's presidential election. Out of necessity, the two wings worked together during the 1950s, when the Republicans were ascendent, but the 1960 election marked the start of the modern switch.
Kennedy was a progressive, Northern Democrat in a way the party hadn't seen before from a president. Four years later, LBJ, though a Southern Democrat, was seen as the standard-bearer for civil rights and other progressive actions. Barry Goldwater, the Republican candidate, was the first arch-conservative Republican presidential candidate, someone we would recognize as from the modern Republican mold. Goldwater won Southern states while LBJ won northern ones, and the switch was well under way.