Fans of the New York Jets are a strange group. The normal fandom split when I was a kid went along these lines: Yankees and Giants; Mets and Jets. The reason is simple, the Jets played at the swampy dump named after William Shea; the Giants played at Yankee Stadium until Giants Stadium was built; the Mets and Jets were the new NY teams from the early 60s; the Yanks and Giants were the venerable long-time NY teams, and were the flagship franchises of their sport from the 1920s to the mid-60s.
That split is less pronounced now. The Jets moved into Giants Stadium in the '80s. And as the Mets took the mantle of the city's top baseball team in the mid-to-late 80s (which the Yanks would reverse in the mid-90s), the Giants clearly seized the football spotlight by winning the Super Bowl in the 1986 season, ripping off a 12-4 season in '89, and winning another title in '90. Even as the Giants have fluctuated from mediocre to NFC champs to second-tier playoff contender; the Jets have had wild swings between success and failure, thus demoralizing the fan base a bit. The rivalry between Jets and Giants fans is nowhere near as vituperous as Yankee-Met disdain -- The Monk cheered on the Jets in the '82 playoffs when they lost the AFC title game on a muddy Orange Bowl field that Miami had deliberately not covered during a wet preceding week, specifically to stop the Jets' Freeman McNeil; and I did the same in '98 when the Jets dominated the first half of the AFC title game in Denver, only to be drilled in the second half of a 23-10 loss.
But Jet fans are a different breed -- more akin to the rough English football (soccer) fans of Chelsea than the somewhat more reserved Giants fans (Arsenal or Liverpool), or the pseudo-collegiate enthusiasm of Denver and KC fans. And they have at least one strange ritual during halftime of Jets games, which does not happen during Giants games (same stadium, different ticketholders). Read the NYT article linked to this post for more.
One hint: think catcalls heard often during Mardi Gras.
No, I wouldn't take my kid to a Jets game either.