[There was a video here]
And here's the current commercial, straight from the State Farm YouTube channel:
Thus the question is: Why the cut? Perhaps the video had been intended to target the Latino demographic considering the slightly—but not distinctly—Latino appearance of the spokesman and what could be interpreted as a recommendation to speak with your local Spanish family about insurance. Perhaps State Farm reflected and concluded they could open the commercial up to a wider demographic with a simple edit. Even though the Spanish is painfully easy to translate ("La Familia" is "The Family" in English), cutting it keeps the commercial uniformly in English.
And yet, State Farm could have edited the phrase out in order to avoid any implications of drug relations. Crazy, yes, but there is definitely a Mexican drug cartel named "La Familia." Perhaps in an attempt to broaden the brand's appeal to a Latino audience, they associated themselves with The Family by recommending potential clients consult them about joining the State Farm family. In the modern era of Political Correctness, their edit might not be too far of a stretch to purge State Farm of any drug cartel alliances.
However, it could go even further: "La Familia" and the Italian "La Famiglia" are pronounced in a very similar manner, much to the extent that it could be interpreted that the recommendation here is that the Mafia supports State Farm. And yes, that's plain old insane, but any of these ideas could easily be the reason the phrase was edited out. State Farm has yet to make a statement, perhaps because it's only two words edited out of a fifteen second commercial, but it's also possible that none of this is true.
Ridiculous conspiracy theories aside, it remains a strange edit.