I thought of something. Even in the off-chance Katniss is not a woman of color by modern standards, she has been brought up in a society that treats her differently for her skin color - a society where she’s confined to a poorer class because of her skin color. So, say (hypothetically) Katniss is Italian-looking. She is not treated as a member of the privileged white class (the blonde haired, fair-skinned, blue-eyed members of the District). This means the definition of whiteness would have shifted, defining Italian-looking people as no longer white.
I think it’s important that Katniss be portrayed by a woman of color by today’s societal standards because a woman of color would have experienced the oppression that comes from institutional racism, which Panem still exhibits. It also would have been a good opportunity in an industry that rarely casts POC for major roles, especially in films where race is not the main focus.
Katniss is not white, no matter what the exact tone her skin color is. Because whiteness is an experience more than an exact color.