I'm not even sure this is any more true now than it ever was before. Players have always hated managers, and there have been repercussions. Billy Martin's feuds with Reggie Jackson were legendary, and reportedly lead to his dismissal at least once. Bobby Valentine was notorious for clashing with players across multiple leagues.
The Sox did stick by Zimmer and unload the players he had trouble with (Bill Lee and Jim Willoughby for example), but that actually turned out to be the wrong move in hindsight.
Of course, the lack of 24 hour channels dedicated to sports and even solely to MLB might have made stories like these a lot less common...