Thank you David Greenberg (emphasis added):
What's left of the case for Rudy's liberalism relies on three prongs: Guns, gay rights and abortion. But even those positions, seen in context, don't render Giuliani a liberal or a moderate so much as an occasional and tepid dissenter from the GOP line. . . .
Take gun control first. Some people demand that their candidate endorse the right to plunk down a wad of cash anywhere, anytime, for a submachine gun. But for most conservative voters, what matters is a "tough on crime" stance, and if any issue has defined Giuliani's career—from his years as a prosecutor frog-marching corrupt bankers down Wall Street to his staunch support as mayor for trigger-happy cops—it's his conservative posture on criminal justice. . . .
His stands on gay rights also don't quite merit the liberal label. Pundits often note that he lived with a gay couple after splitting with his second wife. But policy stands, not private behavior, define a politician's ideology. (Just ask Sen. Larry Craig.) Yes, Giuliani supports more gay rights than do other Republicans, but he still opposes same-sex marriage and has even denounced New Hampshire's law blessing civil unions.
On abortion, Giuliani, while technically pro-choice, is far from liberal: He favors outlawing what opponents call "partial birth" abortion, backs parental-notification laws and supports the Hyde Amendment, which prohibits federal funding for most abortions under Medicaid.
Update (12/1/07): Michael Medved, who calls himself "unhesitatingly pro-life," contrasts Rudy's position on abortion with those of the leading Democratic candidates:
Giuliani has committed to preserve the Hyde Amendment, banning taxpayer money for abortions; the top Democrats urge repeal and favor federal funding. Giuliani applauded the recent Supreme Court decision upholding a ban on partial-birth abortion; all leading Democrats condemned it in harsh terms. The former mayor supports tougher rules requiring parental notification (with a judicial bypass) for underage girls who seek abortions; Clinton and Barack Obama oppose such legislation. Most significant of all, Giuliani has specifically cited strict-constructionists Antonin Scalia, Samuel Alito and John Roberts as his models for future justices of the Supreme Court — and all three of those jurists have signaled their support for allowing states more leeway in limiting abortions. The top Democrats regularly express contempt for the conservative jurists whom Giuliani admires, and worked against the Alito and Roberts nominations.