The white male gets his generic conservative attitude from working in a system that supports him. He doesn't want it to change because for him, it works. Instead of innovating the government's policies, he would take the more cautious approach of working within the lines as they already exist, because they seem well-drawn to a cohort that has benefitted from their delineation (such as him). That, not fiscal responsibility or religiosity, is the core of the conservative ideal. There is actually much to like in such an ideal, even for people whom the system has not thus far made ascendant: stability, assurance in the knowledge that it has worked for others and could be made to work for you, the advantages of familiarity, the perpetuation of rightly-honored traditions, etc. These aspects will also appeal to the section of the majority that also sees itself as on top, as working within the system they were given to rise to the point they are at. It would be foolish to think that just because of race or gender they will somehow find the conservative ideal unattractive.
They will not vote conservative, however, unless the party redefines itself by reimagining their take on this core value and abandoning some of the traditional trappings of that stance.
In the arena of social policy, they will need to eschew publicly-religious-based moral decision-making. This is not because basing moral choices on religious beliefs is wrong. In fact it is probably the only truly legitimate way to do it. The reason they need to avoid this, though, is that in a non-white male majority, they can't count on establishing a unifying religious vision; the new majority is going to be made up of a patchwork of nominal Catholics, a whole bunch of vying protestant sects, and ever-increasing number of the irreligious who are trying to base their morality on some kind of scientific ground or another. Thus, candidates wishing to appeal to this majority of minorities will need to appeal to the one thing most of them will have in common - the belief in a separation of church and state. It will be fine to mention that a candidate is religious, and to in actuality make decisions based on that candidate's own religious integrity, but the party and candidate must have a wholly secular justification thought up as well. It can be done; you can convincingly argue that abortion is wrong not just from a religious standpoint, but also from a scientific/philosophical standpoint, for example. The other basis for social policy in a new conservative party should be economic - a language of dollar bills that every American intuitively understands. Take a cue from the growing libertarian sentiment in this country - if weed and other drugs could be legalized and taxed to turn a profit, then they should be. Let the individual decide what is right for them if it only hurts them - a true conservative sentiment if there ever was one. This coming change is as inevitable as Prohibition's repeal was in the 30's - don't let the Democrats get the jump on this message. Couch it in terms of reacting to the situation as history dictates you should, thus enshrining the move as a move from the heart of your conservative ideal - the idea that we should act based on what we know already works. This will steal the show from the Democrats for the young electorate and truly move the debate about the war on drugs, our border, and the national debt forward into new and fruitful territory - all in a way that preserves your conservative ethos.
In the arena of business and fiscal policy, the Republican party desperately needs to cease its big business protectionist tendencies and become the friend of the entrepreneur, the nascent Green Economy, and the Internet. Teddy Roosevelt was once a member of your ranks; this man is a ghost from your past whose policies are writ large in your political future. Nobody in America likes that we have businesses that are actually "too big to fail." Deregulate - stand for a more open economy so long as trusts and monopolies are not in play. Keep arguing for a smaller government - the nightmare of Greece's downfall is strong in our memories, or could be made strong - but be willing to compromise here (look to cut defense spending, foreign aid, and the postal service instead of healthcare policies, for example). The Green Economy will need some incentive to get started, but not as much or of the type that many Democrats think it will need if a conservative agenda of deregulating the economy and busting up the big players is successfully pursued. Focus emphasis on the improvement of American industrial infrastructure via our Internet - bust up the cable companies, make sure Google and the rest are keeping the net neutral, and ensure it remains the wellspring of entrepreneurship that has made it so huge thus far. Divorce the party from SOPA and the RIAA as much as possible given recent history and use the idea that an economy driven by information technology will boom on a glut of FREE information. Stand against regulation of this most important of business sectors, and be ready to disagree with Democrats on the degree to which governments should have oversight into network traffic and censorship. Some of this does constitute an about-face for the party, but characterize the party and the candidates as disparate instead of united; show that the party candidates who uphold these and other policies are united in ideology but are willing to try to realize it in different ways. This will give the party's image some vitality and dynamism. Liberals will be forced to pay attention to each candidate instead of dismissing them as "Republican." Conservative voters will find the party more inclusive.
Where foreign policy is concerned, Republicans should foster a revolutionary approach with roots deep in American history. Americans are psychologically ready for an era of political (but not economic) isolationism. We should be the country with open borders for immigrants of all colors, with little cause to be involved in foreign conflicts or peacekeeping operations unless called to do so by NATO or the United Nations. The War on Terror can be fought via cunning realpolitik diplomacy with other nations, especially China and India, and by an expansion of the CIA, as we did during the Cold War. Propose to lead the free world by example and not by fiat. Make it clear the USA is looking for profitable business opportunities regarding our planet's climate change and the dawn of Peak Oil.
That last point brings us to the Republican party's relationship with science. The future of the world is one in which science and technology will make an ever-increasing impact, which makes intelligent and coherent use of these tools an imperative for any political party. The reality of Climate Change and humanity's role in it must be acknowledged, as must the possibility that peak oil is upon us. These two events constitute an enormous problem for our developing worldwide civilization, and the Republican party's relevance must consist in engaging with these realities instead of denying them. There are valid conservative approaches to this: focusing on conservation and renewal of natural resources as opposed to major terraforming initiatives, for instance, or championing nuclear power as a tried-and-true green technology with downsides that can be mitigated at a later date by human ingenuity. Actually coming around to the fact that we will need to cut back and be sustainable instead of a forever-expanding industrial revolution. Democrats are lacking in this area because they aren't putting enough emphasis on conservation and sustainable growth, and they tend to wrongly link their strategies to unhappy social policies, such as various forms of population control. They are surprisingly unable to mobilize social responses that Republicans could happily adopt; for instance, the victory gardens and DIY projects which characterized America's incredible response to the stresses of the Second World War could be used to greatly improve sustainable living in America, as would initiatives to move the middle class out of sprawling suburbs and into more densely-packed urban areas that made use of the extra space to create "green belts" in which the ongoing green revolution could develop in close proximity to the people. An emphasis on at-home production instead of reliance on imports would help us avoid the inevitable rise of costs in shipping that will attend the oil crisis in the years to come. American agriculture, manufacturing, and information technology should be bolstered with improved educational outreach to the millions of new immigrants more open borders would provide - these people should be turned into the newly-revitalized blue-collar class of the twenty-first century, ready to actually implement what we have the know-how to do. It is one thing to promote science and technology in our schools, but businesses today know that America's true lack in human resourcing is in the blue collar area. Science and technology are changing what blue collar looks like, but our preconceived notions of its inferiority are unfortunately not. Republicans should make life easy for high-tech blue collar workers, and help resurrect that kind of practical middle class.
America could benefit greatly from a Republican party that stands for the entrepreneur, the individualist, and the sustainable lifestyle. Some party members already have inklings of putting their feet through this door; Romney was really a moderate defeated because of being backed by a rabidly right-wing party that in all probability was the driving cause behind him saying some very unsavory things that voters (like me) just couldn't stomach. I suspect the same was true of McCain, the last time I voted for Obama. Obama is a great president, but it would be great to see a new kind of Republican the next election competing with whoever is tapped to succeed Obama. A Republican prepared to be competitive and radical - only in the sense that they are rethinking what always has made the conservative approach appealing. That Republican could stir up the new majority and do major good for the country and its world. In a future that looks to change our lives so much, so rapidly, we could all benefit from a powerful voice for conservative nation-building philosophy.