In fact you can learn culture without agreeing with it or doing it. Cultural values form a part of our value systems... people sometimes say that I am more Chinese after a long time in China. But, I will never be completely Chinese as there are many cultural values that run deep and form a part of character... you can even talk to people sometimes and get them to admit the logic of something without them leaving a contradictory ideological position.
In my opinion, they are closely related to each other. As a language learner, you learn a language as well as culture of another nation, so that you could communicate with them soundly. Culture is deeper and more sophisticated than language.