First you say you are interested if he makes fun of white people, and when it is pointed out that he makes fun of white people, it is not interesting because then he is just making fun of "privileged" groups.
Clarkson makes fun of everyone, himself more than anyone else (call that privilege). That is why he is funny.
You don't seem to understand why the two cases aren't comparable. There's a huge difference between making fun of a group that you belong to and making fun of other groups. You can't excuse racism just by making a few digs at yourself.
>and when it is pointed out that he makes fun of white people
He doesn't make fun of white people as such. Making fun of Germans for being German is not the same as making fun of white people for being white.
Clarkson makes fun of everyone, himself more than anyone else (call that privilege). That is why he is funny.