Tony's bad rep goes back to his Major Junior days, and I'm like 95% sure that it sources back to cultural differences. There was a podcast with some Rangers AHL coaches a few months ago that spoke about Tony's development, and they inadvertently confirmed my suspicions. Tony is the quintessential emotional, loudmouth idiot you find in working class Italian neighborhoods around the Northeast. He means no harm, but his personality is alien to the good ole Canadian understanding of what a hockey player should be. So he didn't get along with his coaches, which led to him being traded away from his OHL team and then his original AHL team.
When he finally made it to the NHL as a Ranger, he was infamous for making undisciplined, boneheaded plays, especially in tense moments. Then we found out that he's an unapologetic MAGA Republican (like as if a very large chunk of the league isn't), but Tony posted about it on social media, so the pearl-clutchers readied the guillotine.
The final straw in NY was a fight that he got into with Georgiev, which, we later found out, was Georgiev's fault and that Georgiev was the real asshole in the Rangers' locker room. Since signing with Carolina (and maturing both as a player and a man) Tony is clearly more even-keeled and developed as a hockey player. But the Reddit crowd will never forgive him for his tweets a few years ago.