Perhaps a good example of this might be translations of religious texts into modern languages, such as the Bible into English. You roughly have a scale from literal word for word translations (e.g. King James Version) to those which attempt to evoke the depth of meaning of the original language (e.g. The Message or the New Living Translation). There are also translations for specific cultural groups.
Concerning social and human topics, to translate is alwiays to interpretate. Culture is esential for interpretation of ways of living, feeling and thinking. Then culture matters for translation.
Cultural variation affects the way we understand and convey translation. To give a simple example our teachers used to give us: imagine a man comparing his beloved to a summer's day in Iraq (where summer is the worst season ever). What would her reaction be? Shakespeare's summer is not our summer; it's cool and lovely unlike what we have. People have different perceptions for things in different cultures and that includes social values, attitudes and even technological advances, you name it. So, yes, culture understanding is crucial in translation.