I'll let some of the New Yorkers to weigh in on this and offer deeper insight. This issue was raised a few years ago in one of the threads if I remember correctly.

I always associated the Giants with the Yankees and the Jets with the Mets because the Giants played at Yankee Stadium while the Jets played at Shea. The Jets and Mets also came into existence around the same time, long after the Yankees and Giants. I would guess perhaps at one time there was affinity between the football Giants and baseball Giants when the latter made the Polo Grounds their home.

I would associate the Rangers and Knicks with the Giant/Yankee base as these Madison Square Garden teams have deeper roots than the Nets and Islanders. However, pizzaboy and Lou follow the Mets and Giants, Geoff, MaryCas and Babe follow the Yankees and Giants and Irish follows the Yankees and Jets. My wife's family are diehard Yankee and Giants fan, but they split over hockey and basketball, none of whom are fans of the NY teams.