You are misunderstanding her point.
Anne Frank's story doesn't have White privilege because she was White (although that makes it more comfortable for White American kids). Because a story by itself is neutral.
Stories don't have "race". But we don't treat all stories the same.
If you are European, some stories, like what your grandparents really did in the Spanish Civil War. Or how they wound up owning the bakery that was owned by a Jewish family before the war. Those stories are forgotten because we have the privilege of not having to remember them.
When it comes to the "Third World" we also have the privilege of deciding what stories we will tell ourselves. In our White privilege we get to decide what we will remember and what we will forget.
So, in Texas they teach their children to "Remember the Alamo" and celebrate their "Independence Day" from Mexico.
But, they leave out the part about how they betrayed their oaths of citizenship to Mexico and rebelled against the Mexican Federal government. In order to keep their slaves.
That was the "freedom" they were fighting for. The "freedom" to keep their slaves after the Federal Government abolished it nationally.
Being able to pick which version of the story becomes part of the national mythology is "White Privilege".
We don't treat all stories the same.
Anne Frank's story is privileged in the White world. It's a story that we have made very important to ourselves.
Anne Frank "the story" has become part of our Western narrative. Not Anne Frank the real person, but ANNE FRANK the secular humanist Saint. ANNE FRANK as a symbol.
Because the real Anne Frank hardly matters anymore. Her name and face are now symbols and we have mythologized her. Just like Jesus, Mohammed, Ghandi, MLK, and others the mythology around her is more important than the actual person.
We like her story, we find it inspiring because it says that you can be oppressed and hold onto hope. That you can suffer but not be filled with hatred and anger. That even in the worst of circumstances there can be joy and love.
It's not a bad message. But there are other messages and other stories.
I'm Jewish and I find the way she has been deified, in a country that wouldn't take in Jews before the war, to be somewhat odd. Putting Anne Frank on a pedestal in many ways is how White America deals with its Antisemitism.