People can change -- I did!
For a certain period of my life I sincerely believed that homosexuality was a disorder (even if an inborn rather than acquired one) that could and should be "cured" once the right therapies were discovered. I mocked homosexuality whenever the subject came up -- not in the presence of gay people, but around people I knew well. In those days, there was no stigma attached to such talk. I'm embarrassed now whenever I think back on that, but I'm not going to pretend it didn't happen.
At the time of the Iraq invasion I strongly supported it. The risk that Saddam might actually be developing WMD seemed too great (in fairness, he himself was working hard to give the impression that he had something to hide -- he was trying to deter Iran). As it became clear that the invasion had been launched on a false premise, and as the staggering incompetence of the administration's (lack of) planning for the occupation phase came to light, continued excuse-making for the mess became untenable.
Like many intellectually-curious people, I went through a phase of taking Ayn Rand seriously. The sledgehammer forcefulness and clarity of Atlas Shrugged has a natural appeal to a young person who has not had time to think carefully, rather than just vehemently, about social relations and what factors really go into making some people more successful than others. The blindness and hypocrisy (and danger to the actual freedom of most people) inherent in libertarian dogma -- it took time for those things to become obvious.
Earlier still in life, I was convinced anarchy (statelessness) could work in the real world. I sided with the Arabs against Israel. I believed that some human races were genetically inferior to others (though I must say I was never a hater). What can I say? In those particular cases, sheer ignorance of the relevant facts was the whole explanation. I changed my mind as I learned more.
I don't believe my experience is unique. The common thread in all the absurdities above was lack of relevant factual knowledge, and an overly-simplistic view of the world. These are failings which time tends to correct, if we let it. That's probably a big part of why, contrary to popular belief, most people become more liberal as they get older.
Rob Portman's change of heart on gay marriage has been mocked in some quarters because it was prompted by the discovery that his son was gay -- shouldn't he have been able to see the light without needing a personal connection to drive it home? But this is how epiphanies often work. Most people don't seek out information that conflicts with their established views. But they can consider it if some personal circumstance forces it on their attention. Lynne Osterman describes her earlier anti-gay-marriage vote as "politically expedient", implying that she was not sincerely prejudiced but felt compelled to vote that way to support her party. Now, for whatever reason, her conscience and decency have won out. The practical result is that an enemy has become an ally. We'll take it.
In considering the changes in the country that are working against the Republican party, we tend to be so focused on ethnic groups and their relative numbers that we overlook the far more rapid and significant changes which have nothing to do with ethnicity. The exploding numbers of people with no religious affiliation (now up to 20%) and the rapid shift in favor of gay marriage (now 58% for and 36% against, almost the reverse of a decade ago) are examples. Those changes aren't happening because of liberals out-breeding conservatives. They're happening because millions of people are seeing the light that they didn't see before.
Why? In these cases there are obvious explanations to hand. The blunt and aggressive "new atheist" authors like Dawkins and Hitchens have made the malignancy and sheer ridiculousness of religion impossible to ignore. With more and more gay people "out of the closet", especially among the young, more and more people know that this or that friend or relative is gay, making the old stereotypes and hostilities untenable -- let a million Rob Portmans bloom.
This is how we will win the country. Yes, some right-wingers are hard-core fanatics who will never change, but millions of others are reachable.