In some circles ( Native American for instance) the person can claim to be part of the identity if they are as little as 1/16 of that ethnicity.Her small American Indian heritage is not being disputed. What is being debated is she is lying about being part of other ethnic groups that she is 0% a part of.
Have you seen her rants about white people?
Where is the crime here?
She lied on a government document, for starters. More importantly, her deceit has hurt the people and the causes she claims to be supporting. She deserves ridicule.
She could have said, "I have black siblings and children. I studied these issues because I'm interested in them," and then continued to pursue the same jobs and volunteer positions. It would have actually been interesting--maybe even unusual/refreshing--to have someone with her perspective be an outspoken advocate. It would have helped racial harmony, I think. Instead she harmed all of that by lying.