I hate the Giants more than any team in any sport(tied w/ duke basketball). I will root for any team over the Giants whether it's preseason, reg season or postseason. That organization HATES the Jets, they are frauds portraying fake "class" and they bash the Jets at every opportunity. when they were going for their 2nd SB over NE they were tweeting about the Jets. I despise them as much as anyone could despise any team. On a side not I do happen to like some of their players- specifically Eli who is a very good guy but I despise that organization.
RE trying to portray class, is that the organization itself, or fans/media personalities doing much of that? i honestly don't remember the organization itself showing any ill will towards the jets in that regard. the only thing i can remember is when they decided to do a secret coin toss with goodell over who would get the 1st game at the new meadowlands, without jets brass being present.
and in regards to the twitter thing.....bro, you and I would probably agree on my view that twitter accounts for sports teams in general are cringeworthy and a joke, and aren't run professionally at all......but I would use a team's twitter account as the last thing to determine how much 'class' an organization has. nobody high up runs those accounts, it's probably young people who have no sense of what it means to be professional, or to make tweets worthy of a professionally run NFL organization. it's akin to a person of hilary rodham clinton's stature making a 'delete your account'-type tweet
just a couple of years ago the atlanta hawks twitter account made a tweet of worship towards Lil B the Based God. I don't think I've ever seen something so ugly in my life, but it's what you see from team twitter accounts all the time nowadays. it means nothing