None of that has anything to do with how he was as a player.
He was a star and a better player than a lot of players already in the Hall of Fame.
Yeah, but he's also openly made comments about NHL owners/management/teams, NHL players and the league officials that are likely the cause of him being blackballed. He's been making such comments long before social media. Not all of it is openly on the internet, but there's definitely many snippets in old news paper articles, excerpts in his book etc.
I don't know if the league really wants a guy in the HHOF that makes unverified claims that he failed like 13 drug tests but that the league didn't want to suspend him because he was a top scorer. That or that the league/owners etc. turned their back on him for a variety of reasons that are unsubstantiated.
The current twitter stuff isn't a direct reason, but perhaps insight into the level of opinion and commentary that certain people hold against him. He's also the type of guy who will excitedly jump on any soap box he can get on and start sharing his opinions. Fleury is also the type of guy that if he loves you, he really loves you. But if he scorns you, he will do everything in his power to ensure that opinion is known.
I think Fleury's play is of the calibre to get into the HHOF. It has nothing relating to me, but with the people he's attacked, the bridges he's burned, I can see why many former NHL community members want nothing to do with him.