The data is all right there in the study linked to in the article, the full title of which is:
'U.S. Teenage Pregnancies, Births and Abortions: National and State Trends and Trends by Race and Ethnicity'
So let's look at the national numbers and then move to the top five and bottom five states.
The national rate of teen pregnancy is 71 per 1,000. But there are large disparities between races. Nationally, the black and hispanic rates are nearly identical, at 123 and 125 per 1,000, respectively. The national white rate is about one-third of that, at 43 per 1,000. The highest recorded white rate in the nation is in Arkansas, where it's 67. The highest black rate is in New York, at 149 (all of the top five highest black rates are in blue states). The highest Hispanic rates are all in red states in the south, topped off by Alabama at a whopping 228.
So let's look at the top five states for teen pregnancy. They are, in order:
New Mexico, Nevada, Arizona, Texas, and Mississippi. Three are red states, one blue, one bluish-swing. Interestingly, numbers one and two are the bluish states.
New Mexico is number one, at 93 per 1,000. If we break it down by race, we see that the white and hispanic rates are pretty much normal (44 and 127). The black number is actually quite low, at 79. So why is New Mexico first?
Demography. It's 46 percent hispanic, making it the most hispanic state in the nation. Even though the state's racial teen pregnancy rates are normal, its demography is not characteristic of the rest of the nation and thus its teen pregnancy rate isn't.
Similar situations with the rest of the top five. Nevada has incomplete racial data, while Arizona, Texas, and Mississippi all have large non-white populations. The white teen pregnancy rates in these states are a bit higher than national white rates, but still well below the national teen pregnancy rates and significantly lower than the rates for other races in these same states.
Now for the bottom five. They are, in order:
North Dakota, Minnesota, Maine, Vermont, and New Hampshire.
You can see what these states have in common. They are noted for their lack of diversity (four are blue as well). Minnesota actually has one of the highest black rates in the country, but its white rate is low and blacks are only a small share of Minnesota's population.
An interesting comparison is between New Mexico (number 1 in teen pregnancy) and Vermont (number 49). Their white rates are nearly identical, at 44 and 40, respectively. But they are on opposite ends of the list because Vermont is almost all white, while New Mexico is about half white.
I think there is probably some connection between a state's politics and these rates. But looking at the data, the main factor in a state's placement of the list seems to be demography.