it's more important to keep the name of a dead dog accurate, than it is to not alienate any black people who watch the movie?
Yes. Because if you feel alienated by the name of a dog that lived and died 70 years ago who was named for the colour of his fur, that's your problem.
If you have an issue with the word, then it begs the question of why you don't have a bigger issue with the use of the word in other areas, like rap music and other films like Django Unchained, where it's significantly more common.
And if you're going to go and watch a film on a historical event then surely it's worthwhile to maintain historical accuracy and respect the culture of the time.
And ultimately, whatever happened to 'sticks and stones can break my bones, but words can never hurt me'?