FFC included that storyline into the film to show how the Sicilian mafia operated. The trials of many Corleone mafiosi showed some of the powerful bosses had married their first or second cousins. Michele Navarra stands out as he married a Cascio which he was already related to. Navarra was killed in 58' and the two trials in the 60s went into details, while the 1970s trial showed two Corleone bosses being related to Navarra through the Cascios. Plus during the big Maxi Trial, it was revealed that a third of those on trial had married first or second cousins. Given that information, and the time they were making the movie, FFC found that interesting and included it in the movie, but he executed that storyline poorly. Palermo and Trapani providence have high rates of intermarriage. Gambino and Castellano is a well know and talked about in many cases. Imagine what would be said about the Godfather movie if they included the abortion storyline of Lucy or Fredos kids.
Yeah even today it's part of the Calabrians' and Sicilians' clannish nature. Often arranged by the parents, to strengthen family ties and to preserve power. For first and second cousins to marry in Sicily requires dispensation from the local archbishop.