I guess when I first opened up the thread, I was looking at it from an academic perspective. I've met history PhD students. It's a thankless job. My friend's wife recently dropped out of a program after 7 years because there was no end in sight and no job prospects beyond that. And she's a white woman studying European history.
In my field (biotech), to mirror the obgyn analogy before, you'd never tell someone they were ill-suited for cancer research or diabetes research because their family wasn't afflicted by the disease. "You didn't live it, you couldn't understand" is obviously true when working with patients of rare diseases, but it doesn't stop people from pursuing those research areas, and it doesn't make the families any less appreciative when they see the fruits of your labor. You do the work, you're the subject expert.
With the added context of the genesis of the exhibit, her superiors at the museum (and final gatekeepers of content) being educated black men and women, her support from inside the industry from notable contributors, and her history of well-regarded work on various aspects of African American history, I'm inclined to say that her work is probably more important than the optics of her whiteness being attached to it. If there was a danger of her diluting the experience due to her lack of perspective, I'd like to think that someone would've brought it to the museum's attention in the past decade.
Remember, she wasn't hired for this exhibit. She was hired 15 years ago because she's apparently a hell of a researcher. Asking the Smithsonian to hire more blacks is certainly fair; saying that the white employees in the building can't be customer facing is not. If she wasn't headlining this, it would be something else directly speaking to the black experience in America today.
When this exhibit runs its course she'll move on to the next subject, whatever that may be, and I should hope that she's not put off from chronicling and collecting the AA experience after this backlash. Because I think we can all agree, that this shit is fucking important.