Well, a web search turned up this as the first result:
That's a meta study, and the only study they cite which mentions any control group only controls for depression. None of that controls for community engagement/health/connections, which is what I argue is the true problem. I would need better evidence than this.
Not only that, but it seems that this study at best only establishes correlation, not causation, nor the direction of causation.
Personally I arrive at 100% by deduction
The study you cited only lists a 33% change in drug use:
"In their study, Chen and VanderWeele (2018) found that people who attended religious services at least weekly in childhood and adolescence were 33% less likely to use illegal drugs."
Now it has been a while since my last statistics class, so I don't recall the exact methodology to determine likelyhood of causality between these two lines, however just from a quick glance these two rates seem to have a low/medium correlation. They wander closer and farther apart over the 20 years of this graph, and it seems that the drug death rate precedes the religious affiliation rate, which is the reverse of what we would expect if religious affiliation was causing drug deaths.
This all has made me curious enough to do some napkin math myself. Now this is incredibly terrible methodology, but if what you say is true then it should be apparent. I charted countries by irreligiosity, christianity, and drug use, and it doesn't look like there is any correlation:
This is a graph of irreligiosity vs drug use. There isn't much of a correlation here if any. If being an atheist/agnostic/none/etc made you more likely to be a drug user, we should expect a nice smooth rise in drug use correlated with atheism. But that's not what happens here in this chart.
This chart is basically the same thing, but ordered by how christian each country is. If christianity/Jesus/god was anywhere close to 100% efficicacy against drug use, we should expect to see a similarly nice smooth graph, correlating drug use inversely with christianity. But that's also not what happens here.
So if you're right, that it is a 100% rate, if your deduction is correct, then why don't we see trends that support that?
Whatever the methodology, though, claiming that "their success rate is no better than chance" is a lie based on a downright anti-Christian bias.
I definitely have an anti-christian bias, and I will readily admit that. However it isn't a lie, nor is it based on my bias. If I recall there was a leaked report from AA floating around somewhere online from AA, they did a study to see how effective their program was, and discovered it was no better than chance. I'll see if I can find it another time when I get the chance. For now this has already been a lot to compile, especially the two charts I made.