The "we" is referring to black people.
She said she doesn't feel like she can say "we" because of her appearance, she's not dealing with the discrimination a person that looks black would get.
If she's sitting on a park bench in a nice neighborhood, no one is questioning why she's there.
If there's a club that's not letting black people in, she's not getting stopped.
She gives a cashier a $20 bill, the cashier isn't questioning if it's counterfeit.
If she was walking down the street hand in hand with a white guy, no one would think that it's an interracial relationship.
She understands that her appearance gets her passes that other black people don't get. To her, saying we would be unfair to those that have to battle the discrimination that people are fighting against.