I'd say first and foremost your reason for believing that the "right wing" as you define it is large to the point of being significant is mistaken. After the 2000 election, Karl Rove was a major proponent of the strategy of playing to the base, and using turnout to offset the losses in the center (which the Republicans didn't really effectively lose until 2006, as the Democrats responded by playing to their base, just less effectively).
And what is the base? It is the loyal Republican voters who respond, as an aggregate, to certain policies. This does not mean that every, or any single member of the base actually cares about each individual policy. The trends are significant if you look at the group as an aggregate, but as there are different people within the group, and not clones, they believe different things, and value different things, and the group trends don't apply to the individual.
The mistake you are making is this:
"There is a group. By and large they respond positively towards pro life, pro tax cut, anti gay, pro hawkish international policy, pro hunting, anti gun control, anti separation church and state, pro death penalty, pro mandatory minimums, and so on." and equating with "There is a group. Everyone in the group is pro life, pro tax cut, anti gay, pro hawkish international policy, pro hunting, anti gun control, anti separation of church and state, pro death penalty, pro mandatory minimums, and so on."
It's a mistake, because it views people as all exactly like the groups of which they are members. I know a lot of republicans, and I am yet to meet a single one who agrees with everything that the Republicans support.
And politicians play to extremes, as if you act extreme no one's going to question if you're genuine. That also must be taken into account.
I am a Libertarian, a socially conservative Libertarian. I believe in the importance of tradition, of intimations over revolutions, I believe in the importance of a strong military and peace through strength, I believe war isn't pretty, and thus sometimes **** like torture is going to be necessary. I am morally opposed to abortion, although I think it should be legal. I believe in intelligent design, and I think that schools should have to at least acknowledge "We don't know anything scientificly about God, Gods, or the creation of existance, if existance was ever created. As a product of this, in what we teach, it is always possible that it could be a product of some sort of deity, just as it could be possible that it's just a product of natural forces." I support faith based charities, and governmental funding of said charities as long as a clear pluralistic standard is held to and followed. I oppose gun control almost entirely when it comes to actions made to prevent law abiding citizens from gun ownership (or even making it less convenient for law abiding citizens to get guns, as this is a disincentive to gun ownership), although I believe in gun control as far as holding people responsible for any act of irresponsible gun ownership, basically it's your gun, and you're responsible for where the bullets fired from that gun end up. I'd say most gun owners wouldn't have a huge problem with this approach, as most have a firm grip on the importance of responsible gun ownership.
Now I do differ from your perceived social conservatives in certain ways. For one, I smoke a lot of weed, and support the legalization of weed, along with coke, heroin, and so on. That being said, I support legalization in a controlled matter, and shifting the war on drugs funding into rehabilitation, education, job training and job placement. I am opposed to mandatory minimums, although not as much when we're dealing with child molestors, because if you molest a child, there's a significant risk that that'll **** that kid up enough that he'll become a child molestor, and if we catch you, we cannot risk you doing that to anyone more, and as much as it sucks, considering all the reasons why people feel sorry for child molestors (as most of them were likewise molested as children), that's too bad, we're gonna lock you away and throw away the key.
I'm also what I call conservatively progressive, which is to say I'm supportive of the advancement of equal and equitable treatment for minorities, women, and homosexuals, but I also believe that for any true progress to be made, it must be intimated to our social traditions, instead of simply trying to change how things are done entirely. For example, I'm opposed to legislatively changing the definition of marriage to include homosexuals, as I see it as an empty gesture, in that it doesn't fufill the intended purpose, which is to get society to view homosexual relationships as being legitimate adult relationships.
I absolutely want them to close the border to any form of illegal immigration, but I differ from your perceptions in that I am not sure as to what to do with the ones who are already here, because no alternative seems at all sufficient (amnesty just says "**** it, break our laws, we don't care!", guest worker programs would still leave a lot of room for illegal immigration, as it would allow them to not ever get sent back, kicking them all out would be inhumane, so the best I can think of is a process of attonement and contribution to America which eventually leads to amnesty, and any criminality leads to immidiate deportation and being catelogued in a database with fingerprints and DNA.
I also differ from your perceptions of social conservatism in that I am supportive of full observance of the first amendment, including both the establishment and free exercise clauses.
There is variation within any group. If you think about a plane, a group is not a point, a group is a circle around a point, and its members are points that fall within the circle. I'd be closer to the edge of the circle than most, but I most certainly fall within the Republican base.
I believe there are a lot of ways in which Giulianni would promote the ideas of social conservatism, and I think he'd in fact be more effective than most in a lot of ways. For instance, he's pro choice, but he is also a Republican, and so he must not alienate the pro life crowd, and as a product of this, he's in a politically unique position that would lead him to attempt to chart a realisticly middle course which would advance the pro life cause more than any of the jackasses who just stand around and act indignant while trying to pass laws to make getting an abortion more of a hassle. He has a good Republican stance on national security and the war on terror, he's good and tough on law and order, he's acting strong on immigration, and all and all he's good enough.