I can’t find an article in English on this, but today Asahi Shimbun reports that the Japanese government prepared a Q&A document where this point is addressed.
Their position is that if we treat IS as a state, then any action by the SDF on their territory is unconstitutional. However, they are if fact not recognised as such, and hence if the rightfully recognised authorities (Syria and Iraq) give their permission, SDF members could legally take part in a rescue mission as it would amount to “police action.”
I don’t believe either of these beheadings (the one that has already happened and the one certain to happen soon) will change Japanese policy. Whether we can afford or even are capable of doing it forever, I do think that there is a slowly growing feeling in the United States that we need to take a step back from the world militarily. To be frank, Obama’s actions in Libya, in Syria when it was Assad versus rebels, in Syria and Iraq against ISIS has been very restrained. Any more restrained and it’d be borderline open abdication of our position in the world. While some on the right like McCain have clamored for a more robust response, there is significant feeling on both left and right that if anything Obama is going too far with the limited involvement he’s had in these conflicts. The American people are weary of being the world’s policemen, and while I don’t foresee a return to pre-World War II isolationism I think this is the beginnings of a long term trend in which the American people want to see us as at most a “first among equals” in terms of international military efforts and not the guy carrying typically half the burden if not more (often much more in terms of boots on the ground.)
Japan’s military spending is extremely low, even for purely defensive purposes without the Aegis of a robust American overseas presence it’s unlikely that Japan could field a credible defense force specifically with an eye toward China without increasing military spending. [Russia/Ukraine shows what credible means. There is no scenario where Ukraine could ever beat Russia in a war, but Ukraine’s military right after the USSR collapsed was big and powerful enough that Russia would not be doing the stuff it is doing now because to do so would be a bloodbath. But a weak and essentially non-functional military makes Ukraine Russia’s bitch.] I could foresee a genuine need for Japan to buff up their spending on the military, while it was designed to neuter an ultra-expansionist Japanese military the agreements that ended the Second World War also serve to give Japan a very strong military protection in exchange for spending very little money on it. I doubt that situation is sustainable for another generation because of America’s lack of willingness to play this role.
I was speaking as a % of GDP, at 1% it’s what I’d call low. NATO establishes a floor for members of 2% (many violate it), precisely because that’s a pretty good level at which you need to spend to have a military capable of protecting your interests appropriately relative to your size as a country. To be able to credibly look to China as “man, too tough a nut to crack, not worth it” without the presence of U.S. military forces I think they will need to spend higher still.