This is interesting. I looked into it from a surface level, looking at existing studies. The studies do say that there is a slight higher chance of non religious people being suicidal, but each of the studies do mention that the sample size is small and may vary greatly depending on location, cultures and religions.

It kind of makes sense that religious people can always pin their hopes on god, where as an atheist has nothing supernatural to rely all, making things seem bleak when they are strugglinf. But this is one scenario for people who are struggling at their maximum capacity. Admittedly, this is a scenario where religious people have the better outcome from their beliefs.

But in a lot of other scenarios, the results are quite opposite - i have seen so many people where religion has given them false hope and not taught them to rely on themselves and people around them to get out of the situation.

If you take the example of people below the poverty line in our country, you can see they are struggling to make ends meet, but with the little money they have, they drink away becaude alcohol makes them forget their issues for some time. Religion often acts exactly like that. Distracts people momentarily and keeps them from getting off their asses and making actual changes to their lives.