Here's a large study indicating that states with the highest abstinence education level had 25% higher teen pregnancies than states with the lowest level [1], after not controlling for Hispanic teen population, the teen population demographic with the highest birth rate. Whereas, here's one claiming that state policy affected STI rates, but not pregnancy rates [2].

edit: these studies consider "effective" to mean "reduces teen pregnancy + STI rates". Many organizations including WHO consider what they call comprehensive sex education to be a human right, in which case abstinence-only education can never be effective.

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3194801/

[2] https://www.ncbi.nlm.nih.gov/pubmed/26918400

About the first: Correlation does not imply causation. It's very difficult to be sure if the same communities that makes laws to force abstinence-only education also make other laws like forbidding than teenagers get sexual counseling in hospitals without their parents. (And it's imposible to be sure unless you kidnap all the children and put them in two isolated islands in randomized groups.)

Also, they classify the states according to the legislation about abstinence-only education:

0: no mention of abstinence

1: mention, but no promotion

2: promotion of abstinence

3: stressing abstinence as the fundamental teaching standard

It's very interesting that the pregnancy rates for 0 is very similar than 2. 1 is better, 3 is worse. Perhaps the states that don't mention it apply a strong implicit social pressure?

About the second one: I didn't expect this result.

Have you had a look around PubMed?

https://www.ncbi.nlm.nih.gov/pubmed

I also don't know what the evidence suggests specifically, which is why I'd have to do a survey of the academic literature or ask about the consensus.