Hopefully, both should know something, and be willing to learn. The teacher, and here I’m referring to a native speaking teacher, has to know about the student’s culture in order to be empathetic and effective. The teacher should understand the basic differences in beliefs and practices between their culture/the target culture and the student’s culture. They should make every effort to help the student develop the ability to use the target language in contexts that matter to the student, which are usually from the student’s own culture.
But the student is not completely off the hook (=free of responsibilities). The student is learning about the culture along with the target language, even if they are studying the language for practical reasons. Students should be open to hearing about the culture as understood by its members, and they should not rely on stereotypes and preconceptions.