Cartman is trying to find out who his dad is and its not an easy task. First he thinks a Native American is his dad so he dresses and acts as such. Then he thinks its Chef so he acts accordingly.
Regardless, why does he feel the need to act, dress and talk like a certain ethnic group just because his father might be of that ethnic group? Does that change who he is?
If you watch the whole episode you will see that he changes every time he is TOLD who he is based on lineage. Does that make any sense? Yet how many people do just that?