It isn't hard to figure out.
In some respect the Patriots are the Yankees. But baseball is different, especially its history. Lots of people hate the Yankees. But unlike the Yankees they do not have a long tradition that built a romantic, often exaggerated history. Baseball became popular through the newspaper and radio, both mediums were dominated by New York. If you did not live in one of the MLB cities you followed the Yankees or Giants, later the Dodgers, then the Giants moved to San Fran, the Dodgers to LA. So despite many Yankee haters, there are also tons of Yankee lovers spread out there. Baseball also tends to embrace dynasties.
But the Pats have grown one dominant stretch during the internet era where hate, and snark dominate and misinformation and echo chambers elect presidents. Colbert nailed it with truthiness. Who cares if the Pats really cheated, it sounds true enough and fits a narrative. Football's history is largely one of TV, that loves central casting characters. and a simple narrative. "Just win baby" "The Steel Curtain". The Pats win different ways, different years, ball control and defense, high scoring passing attack. And unlike Bill Walsh or Don Shula the genius that runs this show rather than talk at length in self-promotion disdains the media, and seems to hide the charisma he must certainly have. The fact the on the field leader is movie star handsome, married to an actual super model, that embraces fashion not nascar makes an easy target for the tailgating crew. The NFL has built themselves on the "any given Sunday" parity and it annoys many people that one team has overcome this often at the expense of New York teams or the anointed face of the league in the "Aw Shucks" admittedly funny and likable pitchman Peyton Manning. Imagine if the Pistons had kept beating the Bulls? Seriously Imagine if Joe Dumars had 4 rings and Michael Jordan 1 or none?