The Amazing Race has two groups of fans, those who believe that This Is A Race (and prefer intense competition between the teams), and the Call It Karma fans (who watch to see teams they like). They generally get along at the beginning of a season, until something sets them off and the flame wars carry on for the remainder of the season. Arguments about team selection and how the courses should be planned out can get pretty heated as well.
Dark Angel is basically two completely different shows. Fans of the first season have one set of heroes, villains, central themes, and canon; fans of the second have quite a different set with shocking little overlap. Jensen Ackles is an especially polarising figure even in the tiny sect of the fanbase that enjoys both seasons.
Degrassi has a fandom divide between the 'original cast' (Seasons 1 to 7) and the 'new cast' (Seasons 7 to present). While the general rallying cry of the former is 'the Show should have ended when J.T. died', the issue has very little to do with the character. The former believes that the latter cast are poorly hidden copies, the latter believes that the new cast is a superior second attempt. Both sides do generally agree Seasons 7 and 8 sucked.
Doctor Who: The decision to Gender Swap the character in 2017 led to the most extreme broken base scenario in the franchise's history, with fandom pretty much evenly split between those applauding the idea and those who announced they were divorcing themselves from the franchise. (Gender and orientation play no role in this, with just as many female and LGBTQ fans opposed as those in support.)
Whose Line Is It Anyway?: British version (presented by Clive Anderson) vs. American version (Drew Carey). Usually the debate revolves around whether or not Ryan, Colin, and Wayne deserved to be on every episode or whether the lineup should be mixed around more, or who is the better host. But fans will find ANYTHING to argue about, so the Britline vs. Drew's Line debates tend to get increasingly ridiculous — from whether or not (insert cast member here) is either a comedic genius or horrendously overrated, to which country's audience is better (either the British audience is too quiet or the American audience is too loud), to which musician is better at playing the Hoedown music, to which set is better, to which version has better fashion sense.