That reeks more of Japanese xenophobia than of some "Western imperialist racist conspiracy" to destabilize Japan.
That's an alt-right white nationalist shibboleth.
That's no problem of the Japanese, but of the immigrants. They're the newcomers, they're the ones who should be putting all the effort to assimilate into the host culture.
And it isn't happening, not even with descendants of Japanese. Imagine what would happen with a radically different culture (no need to imagine, just look at Europe).
This rigidity and inflexibility is going to be the biggest problem facing Japan when they inevitability reach the population cliff. What you are asking for is unreasonable. There is no way immigrants can ever completely assimilate to that degree. The cultural gap and linguistic distance is simply to big. It doesn't help that Japan has historically been isolationist and based on anecdotal evidence, still seems to be pretty xenophobic. At best, you could hope for a compromise, where the immigrants do their best to integrate, and hosts make compromises and try to be more accomodating. You could try taking immigrants from nearby regions where the gap is conceivably smaller, but politics and history will get in the way.
Ultimately there seems to be no good solutions on the horizon. You will just have to pick the least worst from a selction of poor ones:-
1. Ignore the problem and see what happens. 2. Begin a reasonable program of immigration that suits Japan (there are number of ways to go about this), and deal with the problems that will come with it. 3. Try and hope for some technological breakthrough.
The culturally (and racially) homogeneous state is a myth. Even the Japan you might perceive as homogeneous is the result of many waves of migration stretching to pre-history (Jomon, Ainu, Yayoi, Chinese...)
Places that have relatively open borders (EU, US) aren't experiencing anything like "cultural mass suicide" - unless you buy the nationalist rhetoric coming out of right wing and neo-nazi camps.
All cultures are evolving, including Japan. Sometimes it is gradual, and sometimes it is faster (your example of WWII). Healthy societies accept that change is natural, and try to make sure that it happens in a constructive way.
Meanwhile there's a weird undercurrent of racism, if we just take Japan 2016 and person for person swap out for obviously superior foreigners (imperialism?) then magically everything is supposed to be better. However, in reality, that would obviously not be the case. If an Asian guy is sitting in a broken car, and the driver is removed and replaced with a foreigner, the car is still going to be just as broken. Likewise if the Japanese abandon their land and culture, that doesn't mean anyone else will necessarily do a better job of running the place. Or if there is a better way to run the place, they could save everyone a lot of bother, and implement it themselves.