Not sure I agree with the "respectable players" part either, but for "Baseball has been a game of moral fiber" that could be in the sense that the game has a "moral" thread (one of character) running through it. There are "unwritten" rules to the game that players and fans simply follow but are free not too, if not they get corrected for violations the same way a culture/society corrects members who fall afoul of acceptable moral character or unwritten rules.

Example: guy hits homerun adding to his teams 5 point lead and stands in the batters box admiring his hit before taking a slow excited jog around the bases -- thats just `rubbing it in` and unbecoming. No one who has played the game or watches regularly will blink an eye when his teammate comes up to bat and gets drilled with the baseball -- including the guy hit. There wont be a fight, he wont yell or charge at the pitcher, he will take his base and he'll take care of it in the locker room with the guy that showed up the badly losing teams pitcher.

For an example of a fan violating this see Steve Bartman[0] an especially egregious violation of "unwritten" rules due to the games importance and its impact on the home team while being a home fan

Other sports, this may lead to brawls or petty snipping in the media and resentment which spilled over to fans. Back when the Radiers were in Oakland and Chargers in san diego you'd want nothing to do with that unless you were looking for a fight. Same with teams in the other football sport.

[0] https://en.wikipedia.org/wiki/Steve_Bartman_incident