The issue is that before the Patriots became winners the past 15 years or so there were more Giant fans throughout New England that Pat fans. Maybe friends in Maine and New Hampshire are still Giant fans but they are older folks, but will root for the Pat's unless they play the Giants.
I grew up in Westchester County (NY) and Fairfield County in the 1970’s. There were no Giants or Jets fans. None. Both teams sucked. In school, everyone was an “out of town” fan of the Cowboys, Vikings, Steelers, Dolphins, Raiders, etc. I was Pats a fan. I guess adults were still loyal to the Giants or Jets.
My Dad used to tell me stories about driving from Westchester County up to a bar in Bridgeport or New Haven to see the Giants because of the blackout.