Culture doesn't die out unless people let it. The OVERALL culture of a country can change. Traditional Japanese culture wouldn't be eliminated by coexisting with other cultures. Traditional English, Scottish, Irish or Welsh culture will only die out if people stop celebrating it or if everyone who celebrates it eventually dies out - neither of which are affected by immigration. Some old London family's enjoyment of traditional English cuisine and dances or w/e else isn't affected by a foreign family moving in next door. Similarly, you say the "face" of a country would necessarily change. I'd like to know how you could consider a country's "face" (people's perception of the country?) to become worse through a mixing of cultures without claiming that either: a culture's value is increased by its lessening of proximity to other cultures - if so, I'd like to know why - or that some cultures are objectively worse/better than others, which I am sure that you don't believe.
I'm not talking about better or worse-- but I am talking specifically about the value of culture, and of specific unique cultures.
I grew up in Hawaii, which is a very "liberal state," but one that holds culture and tradition in the highest esteem (which flies in the face of most liberal American ideas). Hawaii is a cultural melting pot (highest multiracial population in the US), so I know what that looks like and celebrate it too-- but what I understand is that in order to respect culture you have to respect the sentiments of the people and the character of the specific culture. This is all about respecting the will of the people in that culture.
This is why I compared Britain to Japan and not China. I am half Chinese and half Japanese by the way-- but I would never make the same argument I did for Britain for China; just as I said I wouldn't make it for the US.
China is obviously a far far FAR older country than Britain or Japan, and arguably with a richer (deep rooted) culture than either of them as well; but China is also a melting pot; it is a culture that has been defined by the fact that its an ethnic/religious soup mix that makes the US looks bland. China has taken over and been taken over by countless groups, and the result is that all of them ended up becoming Chinese. Sure could call the "Han" Chinese as the "true" Chinese race, but it's so muddled and used to co-existing with other groups of Chinese that the idea of further immigration altering the culture is laughable. Ultimately, ethnic or cultural purity is not something Chinese give a rats ass about because their boarders were always too big to protect, and anyone who came in would just be absorbed anyway. That's Chinese culture, and the part of me that is Chinese, really doesn't care at all about immigration to China.
Japan is a completely different story. Japan was long, LONG isolated as a country, and even crushed the Mongol army when they tried to invade. Within the centuries of the samurai and eventual shogunate-ruled-feudalism, they created unique and rigid social structures; like the Koreans, they created their own truly unique brand of Confucianism and traditions honed because of that isolation. Japan is a country whose culture was defined by that isolation, and a "soul" that is still honed by traditions from the Samurai era. While they were the Asian country to most rapidly modernize, they were also the most quick and effective to re-take control of their sovereignty from the foreigners. The Japanese culture is defined by its rigid adherence to commonly understood practices and its ethnic purity-- and yes, when I say "face", I do mean both culturally AND ethnically. For a people whose culture is defined by that context, whose identity comes from it, and who VALUE it-- you cannot simply place black and white on the issue and say you have the moral high ground; when what you propose would essentially destroy the culture within a sovereign country.
People who only see things in black and white are not people who can say that they have a respect for culture--
And I would say an inability to respect culture, and be sensitive to history and context, is an inability to respect humanity.