I can't find any data to support your conclusion, quite the opposite in fact. Here's one study of religiosity by state compared with teen birthrate:

At the level of states in the U.S., conservative religious beliefs predict teen birth rates highly and significantly; the correlation remains high and significant after controlling for income and estimated rates of abortion.

According to this Guttmacher analysis, Evangelicals, and Mainstream Protestants both had about the same number of unintended pregnancies as the non-religious (770, 775, and 752 respectively), while the largest group of unintendeds were tegular Protestants at a whopping 1545. This data is admittedly from 2008, but I wasn't able to locate anything more recent.

Evangelicals did boast the lowest abortion rate for accidental pregnancies at 27% versus 49% for the non-religious.

This article delves into various studies on the topic. Overall teen pregnancy is down significantly from decades ago, but religiosity still affects it.

Unless you can show where the CDC contradicts these studies?