No state bans the marriage of second cousins. Eleven states allow the marriage of first cousins. A few allow the marriage of first cousins if the cousins are past the age of having children, or if one is sterile. The rest of the stares ban marriage of first cousins, and a few consider it a criminal offense.
Marriage of first cousins was not unknown in earlier centuries. In my family tree, I have people who are related to me more than one way. I have distant aunts or uncles who married a first cousin, also a distant cousin to me, so those spouses are my cousins by blood, but my uncles or aunts by marriage.
Re: this accusation against Giuliani — I love it when the left has to resort to pulling things out their @ss.
The Spanish Habsburgs had a lot of cases of marriages between close relatives, which produced Charles II, with whom the line ended.