One of the primary issues people have with time travel stories is inconsistent application of the rules. This is why “old” Doc Brown doesn’t remember meeting Marty McFly in 1955, but does know to protect himself from terrorist gunfire. Or how everyone “remembers” the Black Omen having always been dangling there in mid-air, while the king of Guardia knows absolutely nothing about the priceless artifact that has been hidden in his basement “all along”.
People are generally more forgiving of plot holes like these in time travel stories, since they’re required to make the plot work. Events might be mutable in one scene and immutable in the next. Changes made in the first act might alter the future entirely, but in the second act might instead cause an entire spin-off timeline.
My solution: instead of calling these “inconsistencies” why not call them “side effects of time travel”? Since time travel is an utterly bizarre twist of natural law, wouldn’t we expect it to have some utterly bizarre aftereffects? Throw a huge rock into a lake and you somewhat predictable ripples. But if the lake has an awkward size or shape they will become more irregular and haphazard.
Surely a magic phone booth punching holes in the time/space continuum would have similar irregular effects?