One thing about the Japanese persecution of Christians which I think excludes it from being considered a "religious war" is I don't believe the Japanese government ever use *religion* as an excuse. I'm sure they accused Christians of being foreign agents and traitors to the country but I don't believe they executed them for something like heresy, devil-worship or relgious impropietry. All wars in the end including religious wars such as the Crusades really begin because of power/land/money reasons. What tinges them as "religious" is whether religion is used as a calling card for the ordinary citizens. Just because one religious group in particular is targeted does not mean it is a religious war. For example, in Iraq, the vast majority of dead are Muslims and the invading army is mostly Christian. However, very few people, except conspiracy theorists or religious fundamentalists on either side, will say that Iraq should be considered a religious war. Ditto I don't think that the attempt to colonise China (Buddhists, Taoists etc.) by Christians was really a religious war. I'd like someone to show proof that the justification for execution in Japan given by the government of the time was actual religious and not "they were dirty traitors to the country". Otherwise I don't see how it can be considered a religious war against Christians. A war against what was considered to be invading Europeans with any native Japanese who show any sign of following them, which conversion to Christianity was an obvious sign of, as traitors and collaborators, yes. Religious war, no. Remember, not everyone thinks the same way as you do. Religious justifications for wars is a natural part of Western Christian thinking. So it is natural for Christians to assume that a group is targeted for religious reasons. People assume that other people would act the same they do. However, that is not the E. Asian way. Groups are targeted because they annoy the government. Superstition is despised by the scholarly elite but that's not the same thing as religion and it's not like they'd execute anyone for being superstitious. Religion does not play the same role in E. Asian thinking as it does in European Christian. There is no centralised authority, or even centralised holy book. Religion as practised amongst ordinary people consists mostly of superstition, herbal medicine, fortune telling, whatever gods happen to be popular in the region, folk tales, agricultural festivals and is strongly centered around the family. If a certain monk or priest gains favour amongst a politician a monastery could gain a lot of political influence. But you know what, it has no influence amongst ordinary people. A monastery cannot tell a random village to do something. Monks and priests don't hold sermons or services. They don't even hold marriage rites (at least not in traditional China). They do not have any central role in E. Asian communities. Besides, most ordinary people despise monks who gain power. There are tons of jokes about corrupt monks and priests, dating back centuries. Honestly speaking, the lesson I learn from folk tales and history lessons is that a monk/priest in power is a bad person, because they do tend to be tghe villains in many stories.
Another thing that prevents powerful monks from inciting religious wars is that the people in power tended to be Confucian bureaucrats and they despised monks and priests because as I said the scholarly elite despise superstition. Not to mention monks and priests tended to appeal directly to the emperor and hence like eunuchs was a threat to the bureacrat's power. And they write the history books

Not to mention if anyone needed to actual mobilise the army in a religious war, who is going to have to organise it - the Confucian bureaucracy? They're not going to mobilise for religious reasons. Also I suspect, since the Confucian bureaucracy would be organising the whole thing, they aren't going to be putting a too religious tinge on it. It goes against their grain. If they were to put any cultural tinge to it it would be against "barbarians". Concepts of cultural superiority are much more important and more ingrained than any religious reasons. In fact this was the slogan of anti-Western and anti-Shogunate forces during the Meiji revolution - "throw out the foreign barbarians and restore the emperor". Hell, even the Chinese "ghost-man" to describe Westerners is more cultural than religious. Most Westerners like to translate it into "devil" indicating religious slants. However, it's because you see, Chinese are men - they are civilised, cultured and you know generally well civilised. Something which takes the form a man but is not a man is a ghost. This is emphasised by the fact that the word for "man" or "woman" used in "ghost-man" means an uncivilised hillbilly barbarian. Japanese, Phillipines etc. all have "ghost" appended to their descriptions as well at various times. It's not religious, it's cultural and racial snobbery. This plays a much more important role in justifying wars and persecution in E. Asia than religion does. We can kill them because they are uncivilised barbarians in a very popular theme through E. Asian history. It's not any better than religious justifications but it's not the same thing. A Confucian bureaucrat would be insulted by the very idea of a religious war. How you would even get ordinary people worked up on religious grounds is another matter. How you would get all the monasteries in the country to agree to follow a single line from one monastery considering the compete with each other is another matter. Not to mention they don't have much authority really amongst ordinary people. There is something known as false consensus in which you believe people will do something because you would do it (or your culture I guess). Note that the attempts in Japan to form a national religion and justify massacres, invasions etc. on religious grounds only started occuring after the Meiji revolution when they consciously started to copy Western technology and societal structures.
In summary, religious wars don't have much traction in E. Asia because:
1. Well, religion is very similar everywhere. Buddhism + Taoism + Ancestor veneration + animism and shaminism. There's not really that much to differentiate on religious grounds.
2. Confucianism despises superstition. Also, any monk/priest who gets into power is seen as a threat to the power of the Confucian bureaucrats.
3. Religion is very decentralised. Any monk/priest who gets into power tends to be despised by the general populace who grew up on folk tales of corrupt monks and priests and dire lessons written in history books by Confucian scholars of evil monks and priests who lead astray emperors by seducing them with promises of immortality or magic tricks. So monks who get into power have a serious religious credibility problem.
Also in Japan there is historically strong suspicion of Buddhist monks/priests close to the seat of power due to a previous emperor who nearly ruined the country because of her Buddhist monk adviser/lover (?). This also turned Japanese off female emperors. Of course the history of this period was written by Confucian scholars (anyone see a pattern emerging here?)
4. Racial/cultural superiority is seen as a much better justification for general massacre than religious reasons.