As you said, Ratman, at least BttF was consistent in how it worked. Even Avengers Endgame managed to fuck it up (Loki's escape should've had all sorts of repercussions).
So, there's this entire show called "Loki" that covers exactly this. They went with "bug as feature" and embraced that it should have had repercussions...and why it (maybe?) didn't.
So, I haven't seen any of the Loki series, but I really liked that Endgame at least could fit with a logically consistent branching scheme. I'm disappointed that it sounds like the Loki series doesn't stick to the branching scheme, but I haven't seen it.
Open-loop movies like "Back to the Future" have a mystic one true timeline, and if you stray from it too far there are supposed problems - but it makes no sense because it leads to out-of-sync points -- like Marty disappears from his own photo and his hand starts to fade, but he can see his own head disappear. Not to mention the ethical oddity that it's supposedly wrong to make yourself rich, but somehow it is OK to get a cool and better new life by other means.
In Endgame, the rule that they say is that the past is unchangeable. If you go back, you create a branched timeline. That's a consistent and sensible rule for time travel, and the movie plot perfectly fits with this -- they don't change the past at all, but just use the past to change their own future. The only unclear point is when Steve Rogers appears as an old man. Since he doesn't appear on the platform, some suggest that he rewrote the main timeline and old man Steve was actually around all the time in the background of the previous movies. However, it's also consistent that he lived out his life in a branched timeline, but some time over the decades his suit broke, and he had to use an alternate means to jump back (like getting help from the Hank Pym in his branch).