Oklahoma is not part of the Historically Southern United States. Although, geographically it can be considered part of the Southern US as defined by the US Census Bureau, it is not part of the true South.
I was born and raised in Mississippi and then went to college in Oklahoma. While living in Oklahoma, I found that some Oklahoma residents thought they were part of the Historical South. But as a native of the Historical South, we do not consider Oklahoma as part of the South, whatsoever. Bless your heart if you do.
Below is another map, which shows the South, culturally and historically speaking. It's the states that seceded from the Union. Oklahoma is not part of that. Living in both the South and in Oklahoma, I'd say that Oklahoma has country living, which a lot of the South does too - but it does not have the Southern culture.