"Culture" is a very large and full bag. Some items in it are fundamental to maintenance of civilization, others are entirely superficial.

Civilizational: Respect for rights of minorities, rule of law rather than of the strong, willingness to work and pay taxes, valuing education.

Superficial: Cuisine, dress, artistic taste, ritual formalities of religion.

Few governments have had success splitting immigration policy priorities along these lines, though some have had the wisdom to at least try.