Despite claims that the product is safe, many people have stopped buying it.

despite 是介词，意思是"尽管、虽然"，表示让步关系，后面接名词或名词性短语。这个词来自古法语，由前缀 des-（表示"相反"）和动词 spitter（"吐"）组成，原意是"蔑视"，后来演变为现在的让步含义。