How can one (you) adjust to a new culture while being loyal to your native culture?

Well I honestly would think it would be very difficult for someone to adjust to a brand new culture while preserving their own native culture. It is often very difficult because when taking decisions or making choices you always look through you own native cultural perspective which makes it very hard for a husband or a wife to get along. I think that it would take someone really great to preserve their own native culture as well as a new culture because it will be really hard.