Yes sauerkraut can give you diarrhea as well as stomach pains and stomach cramps if you eat too much of the sauerkraut.
Eating a good quantity of sauerkraut is also a good way of getting rid of and treating constipation because the sauerkraut when eaten enough can get your bowels moving.
But if you don't want diarrhea then watch how much sauerkraut you eat because soon you'll be having diarrhea and that goes for cabbage as well.
Cabbage is another food that while healthy it can give you diarrhea when you eat too much of it.