Just curious to know (I also need this piece of info for writing my novel).
So, can a German Shepherd (classic-looking fur coat) give birth to four identical German Shepherd puppies that look just like their mom, but then, her last one is a white German Shepherd puppy. Is that possible? If it is possible, is it likely that the mother would neglect the oddball puppy?
Yes it is possible! Not common, but it CAN happen.
The white coloring happens because of a recessive gene that can be hidden for several generations before making an appearance. Both parents must carry the white gene to produce white German Shepherd puppies.
It is very possible that two "normal colored" German Shepherds (carrying the white gene) can produce white puppies in a litter of black and tans or sables, etc.
A white German Shepherd is not albino, and should also have both dark eyes with a black nose and lips. White is also considered a "masking" gene which covers up the dog's true color, although it does not affect skin pigment. This is why "white" German Shepherds often have a cream or blond tint to their solid white coat.
Possibly you're just seeing a case in which different puppies in the same litter have different fathers. This is called superfecundation, and dogs' reproductive biology tends to make it happen fairly often, because dogs (unlike wolves) mate promiscuously, and ovulation is not triggered by mating, as it is in cats.
It's also possible that this is just a recessive gene.