When someone says, "I don't hate the people, I just hate their culture," what he or she really means to say is, "I don't hate the people as long as they are just like us."
The only thing that truly distinguishes us from each other is our culture.
We all have the same genome.
To say that you hate a culture directly implies that you take issue with the people of which it is comprised.
Racism and discrimination have never been limited to individuals, and if you have convinced yourself that you can dislike an entire culture without it affecting your opinions of its members, then you are actively fooling yourself.