Most countries who import a lot of labor tend to specialize on a narrow profile of immigrants (Turks in Germany, Latinos in the US, Central Asians in Russia), hence they are not getting cultural continuity. The imported labor clings together and forms a distinct culture.

In this regard it would make sense to eat it up and accept population decline. Japan of 50 million Japanese is still Japan. Japan of 40 million Japanese and 40 million Filipino is no longer Japan. May still be passable country, though.