I was also...well, not surprised per se, but certainly annoyed to see that "Native American" in any form wasn't even an option. One could construe that as revealing, I suppose.

I don't know how relevant the question actually is, but if we want to track ancestry and racial, ethnic or cultural group affiliation, the folowing scheme is pretty hard to mess up:

Country of origin: <drop-down list of countries>
Country of residence: <drop-down list with "same as origin" as the first option>
Primary Language: <Form Field>
Native Language (if different): <Form Field>
Heritage language (if different): <Form Field>

Note: A heritage language is one spoken by your family or identity group.

Heritage group:

Diaspora: Means your primary heritage and identity group moved to the country you live in within historical or living memory, as colonists, slaves, workers or settlers.

<radio buttons>
European diaspora ("white" North America, Australia, New Zealand, South Africa, etc)
African diaspora ("black" in the US, West Indian, more recent African emigrant groups; also North African diaspora)
Asian diaspora (includes, Turkic, Arab, Persian, Central and South Asian, Siberian native)

Indigenous: Means your primary heritage and identity group was resident to the following location prior to 1400, OR prior to the arrival of the majority culture in antiquity (for example: Ainu, Basque, Taiwanese native, etc):

<radio buttons>
-Africa
-Asia
-Europe
-North America (between Panama and Canada, also includes Greenland and the Carribean)
-Oceania (including Australia)
-South America

Mixed: Select two or more:

<check boxes>
European Diaspora
African Diaspora
Asian Diaspora
African Indigenous
American Indigenous
Asian Indigenous
European Indigenous
Oceania Indigenous

What the US census calls "Non-white Hispanic" would be marked as "Mixed" > "European Diaspora" + "American Indigenous" with Spanish as either a Native or Heritage language. Someone who identifies as (say) Mexican-derived but doesn't speak Spanish at all would be impossible to tell from someone who was Euro-American and Cherokee who doesn't speak Cherokee, but no system is perfect...