I’ve done some research. The picture was snapped during the 2008 campaign and the local fans called it as a Patriots hoodie then. http://www.examiner.com/new-england-patriots-in-boston/sarah-palin-outed-as-a-new-england-patriots-fan - is a sample of the coverage then in the New England Examiner.
Examining the comments, I suspect it is a local school in Alaska, not the New England Patriots.
That makes sense. My HS team was the "Patriots" and some of our regalia bore a suspicious resemblance to the NFL team's regalia.