I don't know about the Japanese, but in Europe where this practice was common (certainly in London) one answer is simply that they tolerated more outbreaks of infectious disease.

It's possible to make it safe through composting, but that requires more time and skill than a typical compost heap. Most composting authorities recommend keeping cat and dog faeces - less dangerous than human waste, but much worse than cow manure - out of the garden compost heap.

Having a more or less vegetarian diet helps it some at least - less trophic layers since the diet is more akin to other herbivores although not as fibrous as grazers. Since fish was far less spread before advances in refrigeration and transportation those inland more would have been more subsidence farmer involuntarily vegan - let alone the increased acceptance of meat.