I know the title may seem weird and maybe a little hard to understand, so allow me to explain.
Fairly recently, I debated the value of continuity in the Fred Wolf cartoon and argued that even though the show wasn't very big on continuity, to some extent it must matter because the show isn't a total anthology. Since it follows what are ostensibly the same versions of the same characters, and does indeed make episodes that are direct sequels, then the show can't really afford to have rather heavy contradictions like showing Krang is from a race of Brain-like creatures in one episode and claim he was originally a Reptilian creature in another. The other guy disagreed and went so far as to claim continuity didn't even matter within season 1, even though season 1 is a five-parter and thus isn't episodic enough to defend in such a matter.
While I can understand continuity being kept somewhat loose, like keeping a floating timeline or not following up on certain characters introduced, I find it difficult to believe anyone is so disinterested in continuity to the point where the core plot or the main characters' backstories can be contradicted.
The Simpsons is a show that has never been big on continuity either but what's arguably first episode that was reviled, was so precisely because the episode broke continuity.
So, Is there really no way the show could have broken continuity and you wouldn't have been OK with it?
Here's an extreme example that could have happened:
Let's say the show decided it wanted synergy with the movie because it did so well and didn't bother to explain any of the changes made. Suddenly Splinter started out as a pet rat, the Foot Clan consists of runaway teens, Bebop and Rocksteady are replaced with Tokka and Rahzar, the Ooze suddenly came from TGRI rather than the Technodrome, April now works for Channel 3/Charles rather than Channel 6/Thompson, Casey Jones is now a main character and acts more like his movie counterpart, etc.
Essentially, if the show had become "The Movies: The Animated Series" without explaining any of the changes while still clearly being the same show rather than a reboot or sequel to the movies, would you have accepted that? Because if you say yes to that question, I am really curious as to how you could think such a drastic change would be acceptable, especially if it has no in-universe explaination.