A number of recent Gallup polls have been put together by the polling organization, leading to the conclusion that the most religious Americans have the highest level of "wellbeing". You can find the data here, here and here. The neologism not withstanding, the data can be taken to mean that faith brings you physical and mental health.
And yet it doesn't take a genius or social scientists to poke holes in this conclusion the size of your average megachurch.
To start with, the study is based entirely on self reporting. This problem with surveys having to do with religion never seems to bother religious folks who quote them as they tout the glory brought on humanity by the wonderful institution. You ask someone how religious they are, and in the next breath you ask them how much they drink. What is the likelihood that your next door Muslim, Baptist or Mormon will under-report, consciously or not?
The second problem is that it doesn't take into consideration the benefits of community bestowed on the faithful by their houses of worship. Undeniably that is an area where we have fallen short, even though things are getting better. Having long lasting friendships in the context of service attendance could well be helpful in reducing anxiety and depression.
Another factor possibly skewing the results (and not adjusted for in the surveys) is the location of the most versus least religious. Anecdotally at least, rural areas in the US happen to have the most religious populations, while the least religious live in major urban centers. City life stress, plus other factors affecting urban lifestyle (such as diet and exercise) may also be affecting the findings.
There are other effects of religion on health that are a lot more subtle and cannot be surveyed for. One notorious example is HIV. Condemnation and denial of homosexuality among a number of ethnic and religious communities only leads to delayed diagnosis and further spread of the disease among men and women alike. Other examples includes denial of blood transfusions by Jehovah's Witnesses and faith healing leading to delayed care, which at times can be deadly.
Last but not least, let's not forget the hostility directed at non-believers. The kind of threats that activists like Jessica Ahlquist have to deal with represent only the tip of the iceberg. The social situations atheists face are all too similar: keep it to yourself or put your career in jeopardy and risk shunning by friends, family and community. No surprise that the religion report higher levels of "wellbeing".