For example I cannot trust the leadership of this country, to a person that supports the murder of innocent human beings and condones the lifestyle of the sodomites.Neither would I, but if I understand Giuliani's position correctly, he desires to have these issues battled out in court, not in Congress, and ultimately to leave them to the states to decide. On social issues, I'm more interested in the kind of people a presidential candidate would nominate to the courts than I am their person views. Rudy can be "pro-choice," but if he nominates people like Alito, Roberts, and Scalia, his person views would be of little concern.
I understand your position, but I see holding to a pro-abortion and/or pro-sodomy position as being serious flaws in ones character and morality. Even if a politician would say "I'm 'pro-choice' but I promise to nominate only 'pro-life' judges" I would still withhold support as their personal stance would cause me to have serious doubts in their ability to define moral absolutes. The moral issues are not just about advancing a political agenda, but are defining of ones character.