Race and Hispanic or Latino: 2010--State--Place
American Indian: 321,687
Pacific Islander: 4,369
Other race: 154,409
Two or more races: 221,321
As I noted earlier, Hispanics can be of any race. The number of Oklahomans who identified themselves as Hispanic is 332,007.
True, this number is more than the number of American Indians or Alaska Natives. A mere 10,320 more. But that obscures some important qualifications.
1) People who listed themselves as American Indian may have checked the Hispanic box also.
2) Those who checked "other race" may be American Indian, Hispanic, or both.
3) Those who checked "two or more races" may be American Indian, Hispanic, or both. In fact, according to one Census table, 29.2% of them are part American Indian or Alaska Native.
In short, there's no way to distinguish Indians who counted themselves as part Hispanic or Hispanics who counted themselves as part Indian. Therefore, I don't think we can conclude that Oklahoma's Hispanic population is larger than its Native population. We can say they're close now.
We also can say that Oklahoma remains about 77% white despite its significant Indian and Hispanic minorities. In terms of racial or ethnic diversity, I doubt the state is even in the top 10. In other words, the person who challenged my posting was wrong.
For more on the subject, see 5.2 Million Indians in 2010 Census and Indian Identity Matters to Indians.