"Crops which have evolved over thousands and tens of thousands of years by dwelling together with human beings are not products born entirely from the discriminating knowledge of the farmer, and can be thought of as naturally occurring foods. But the instantly altered varieties which have not evolved under natural circumstances, but rather have been developed by an agricultural science which has drawn far away from nature, as well as mass-produced fish, shellfish, and domestic animals, fall outside that category
." page 127 of his book 'The One Straw Revolution'.
I don't see in this particular book, the only one I'm familiar with, him expressly criticizing the eating of animals. But rather the unnatural manipulation of any food, causing people to be out of balance with nature, and this will always lead away from health, which he touches on lots of times. I think it looks like he saw the eating of animals as perhaps being natural, but not in the mass produced agribusiness way we started to do, getting away from just looking for what our body tells us it wants, and can obtain.
He stresses 'not working', not encouraging laziness but being more natural rather than driven for monetary success and 'hard work' to 'make' nature fit some framework that serves you. Working within the framework that already exists.
A lot of Buddhists are lacto-vegetarian, but I think it's something like 90% of the Asian population that are lactose intolerant, and it was never a big part of Japanese life (til modern times). Considering how violent and unnatural the dairy industry has become, you see more Buddhists and Hindus who used to use ghee and milk going vegan due to this. IMO one could obtain ethical dairy if they do it themselves, but it's harder to do going to a major grocery store and buying mass produced goods (almost impossible). It's what prompts some of the vegans to take the 'abolitionist' approach to diet, partaking in nothing that could potentially give profit
to those industries. I agree with this to a point, but if a personal homestead or smaller farm can ethically give you animal foods that you think you need or that you want, I don't see this in the same light as large producers who are committing atrocities. Even hunting/small scale homestead meat production is different than confining, abusing, and killing for meat en masse in farrowing sheds and windowless barns, too. I think there are clear abuses and then the 'spectrum' of what we think is natural or right starts to become a little different from there for different people/cultures/individuals based on perception of what is natural and what we need. Are we obligate carnivores? Maybe. But which meat would we be likely to kill out there on our own if so? IMO fish and similar, would be the easiest thing for a human to get. We could get eggs, but rarely. That brings in the other question, since we developed farms that gave rise to the ability to house and keep animals and have an abundance of food regularly in exchange for caring for them. IMO if that is how it's done it's not such a problem. It's not a part of the way back machine as far as 'what is natural' is concerned though, but maybe everything doesn't have to be to be healthy. When greed and unnatural practices come into play, there's the problem, IMO, because then you view the animal not as something sentient, but a number, a statistic in your business plan. Same thing happens in businesses that only deal with people, and view them that way.
Fukoka lived to be 95 so he definitely was on to something. He had many books. 'Sowing Seeds in the Desert' and 'The Road Back to Nature' look like good reads. Not sure if they'd have the info you are looking for re specifically veganism/vegetarianism. As for Buddhists though, some will not eat meat and some will eat meat so long as it was not slaughtered for them. They do intermittent fasting and do not consume alcohol either. Some will keep away from certain spices, same as Hindus, such as too much garlic or turmeric. They use those medicinally but don't believe it's healthy to load your dishes with them. I'd venture to say that many, if not most, Japanese Buddhists have been vegan, but used to simply call it vegetarian, since in that region milk wasn't much of a 'thing' in their natural diet and the term wasn't used widely either.