There are some indicators that it does make a difference; too lazy to dig those up, but it should not be surprising that adhering to some religious doctrine that discourages activity X should have some effect on reducing the frequency of X abuse among the adherents (not just the reported numbers, but actual values too).
However, what I wanted to say is more like - if you don't have a crane, yet need to lift an X-wing fighter from the bottom of the swamp, you have to use the Force. Nothing else will suffice. Basically, both the damage caused by substance abuse, and, more importantly, the deeper reasons people stick to it, are so huge, you need to pray for a miracle (and people who believe in God often do).
On the other hand - when you strongly discourage something and decide to make doing it wrong/immoral, you also make it very taboo and stigmatized to talk about, which can be incredibly dangerous.
This is very obvious with illegal drug use and sex, problems related to them (drug addiction and unwanted pregnancies/STDs) are much higher in places where it is strongly discouraged, stigmatized and hard to talk about.
There are a lot of sad stories where people who knew they had a drug problem didn't dare seeking help/talking about it in fear of either the law or negative reactions from the people around them.
Wrong/lack of information about safety is also a huge issue due to making stuff immoral and taboo, millions of people in Africa have died and are currently suffering because of the way extramarital sex and condom use have been (and still are) handled and talked about.
Personally I think complete openness instead of moralization/stigmatization is a much better solution to deal with difficult issues. Granted, I'm a very socially liberal guy, but I think most evidence is pointing to the fact that information and sympathy is leading to more desirable social outcomes than repression and stigmatization.
For example, let's take something extremely controversial as pedophilia. The vast majority of society is of the understandable opinion that being a pedophile is immoral, often downright evil. People unfortunately don't realize how extremely important the different between simply being a pedophile (having sexual thoughts about children) and actually committing such acts are.
I think even something as pedophilia should be freely discussed and that pedophiles should be offered rational stigma-free ways to deal with their sexuality in ways that won't hurt children instead of being treated like scum by society. The way we deal with the issue today is hurting everyone involved - both the pedophiles and children.
A ton of people undoubtedly disagrees with me - and that's understandable from an emotion point of view. However - I've never seen any research or statistics actually indicating that punishing people for their problems (either directly through the law or through stigma) leads more significant positive societal outcomes than helping and sympathizing people with their problems does.
Oh, of course. Far too many people don't realize that religion (in general, and in the "Bible belt" case, Christianity in particular) should be completely orthogonal to such concerns as science and education, and truths revealed therein. There's no inherent conflict, of course; but people from both sides are guilty of acting as if there's conflict. Unfortunately for religious people, they have started it first in ages past, when religion was a standard, and so now they tend to have harder time learning the error of their ways.
"people from both sides are guilty of acting as if there's conflict."
Angsty atheists claiming there are no "true" Christians who believe in evolution or who are evolutionary biologists by trade are obnoxious, but more harmless than those who wedge religion into science classes.
Alcoholics Anonymous famously has "turning your life over to a higher power" as one of their 12 steps. They also provide a very open community. They seem to have some success.
AA is actually about exactly what I'm talking about, they're about talking openly about your problems and receiving sympathy from others who either have similar issues or have overcome them without fear of being judged or looked down upon from others.
That being said I think scientific evidence-based solutions are generally a better option than AA. Don't get me wrong - I'm not disputing that AA certainly has helped a lot of people - but the statistics aren't looking great either.
However, what I wanted to say is more like - if you don't have a crane, yet need to lift an X-wing fighter from the bottom of the swamp, you have to use the Force. Nothing else will suffice. Basically, both the damage caused by substance abuse, and, more importantly, the deeper reasons people stick to it, are so huge, you need to pray for a miracle (and people who believe in God often do).