Firstly, consider what is meant by Health. Generally, we are healthy or something is healthy or in a state of health, when it is free of disease; or does not predispose or helps prevent disease or a pathological state. It is thus defined by what it is not. Humans have a wide variance of functioning though, so we have to assume an Ideal Man as it were. However to define this in practice, we have to take a bell curve and take cut-offs for the mean thereof - assuming that the high and low are both predisposing to something not within what we see as desirable.
So for instance, with blood pressure we know hypertension leads to strokes and infarcts, and low pressure is associated with shock and syncopal events. However, normal functioning for some people might be on the high end, even if in the long run, that might be harmful. Hence we assume a 'normal' blood pressure which we are aiming at, which seems to be the general state in man.
Now most medical diseases and such, work in like manner - especially Chronic ones. When an hypertensive has high blood pressure, this is usually secondary to something - an excessive sodium load or overcome renal vascular occlusion say, though often we don't actually know and term it idiopathic. For that person, it is 'normal' though, how his body's homeostasis works, but is unhealthy when measured against our concept of Health, an hypothetical ideal.
So let us review Atheism by these criteria. Clearly it is not the norm for humans, as universally all cultures have some form of religious belief historically. So already we are dealing with an outlier. Now hyper-religiosity is also used as a symptom of mental illness, but that is because it is one that is highly sensitive to being picked up - someone declares themselves a prophet or so. A hyper-atheism on this same spectrum of belief, would not have any overt symptoms beyond perhaps denying religion or maybe a lack of tolerance toward it. So its sensitivity is low as a symptom. Atheists though, are over-represented in mental health care use, and religion is protective. Numerous studies have demonstrated that religion is positively correlated with better mental, as well as physical, health. For instance:
Religion, Health, and Psychological Well-Being
Religion and health: Is there an association, is it valid, and is it causal? - ScienceDirect
Religious and Spiritual Factors in Depression: Review and Integration of the Research
Non-Religion is associated with poorer mental health outcomes. Beyond that, religious people tend to be healthier in general than their peers of the same diet, lifestyle and socio-economic class who are not. While clear causality has not been demonstrated beyond doubt, the correlation is definite, though a specific physiological mechanism for it has not been found, and psychological theories tend to cluster around ideas of 'certainty' or so, but even there, people with religious affiliation and strong devotion to their religious practices, outperform all on health parameters.
Secularity, religiosity, and health: Physical and mental health differences between atheists, agnostics, and nonaffiliated theists compared to religiously affiliated individuals - ScienceDirect
The Benefits of Religious Fundamentalism
To return to what is Healthy then, Atheism and non-religion clearly have worse ourcomes on measurable health factors and use of medical services. It is also not a natural position for humans to take, as the vast majority of humans throughout history have been religious. We are thus forced to conclude that it is an outlier on human functioning with potential factors predisposing to disease or undesirable outcomes, and our Ideal Man, our hypothetical examplar of health, would be religious.
What of Disease though? A disease is something which produces specific symptoms or a syndromic association of symptoms, that negatively affect health. It is defined by taking factors that deviate from the norm, and to cluster them together, as in my above example of Hypertension or associated sequalae like strokes. A lot hedges on definitions here, but the argument to label Atheism and Non-Religion unhealthy is strong; but are these symptoms of a presumably mental illness, or merely a predisposing malady such as being born with a less effective gene, or unhealthy human behaviour like smoking or a sedentary lifestyle? The argument to label it a disease itself can even be made, but of course, that hedges on what is termed desirable - if we cannot agree on basic desirable outcomes, then all bets are off, such can be seen with transgenderism vs gender identity disorder.
However, being religious is in general better for you. Sure, every now and then we'd have people going off the rails and declaring themself to be God or so, but in like manner, we have people with brittle bone diseases or the ilk, in which healthy exercise would be deleterious.
Encouraging Theism, and more than that, strong devotion, would be a public health benefit. Functionally, trying to advance atheism is akin to encouraging someone to take up smoking or to not have their kids vaccinated.
End Note: Nowadays it is difficult to assess these clearly, so read studies with care. For instance, a US study found the population of atheists they studied (which tends to be younger) to have better dietary practices and be more active, so consequently were 'healthier' than the more sedentary and older religious group. This is why meta-analyses and trying to correct for confounding factors are so important, on questions such as these.
Health and Well-Being Among the Non-religious: Atheists, Agnostics, and No Preference Compared with Religious Group Members
Further to note, most studies are done in the WEIRD countries (Western, Educated, Industrialised, Rich, Democratic), so the religious populations we are talking about, tend to be mostly Christian, with some Jews and Buddhists and Hindus vs the modern expansion of atheism and non-religiously affiliated, which may be a confounding factor.
So for instance, with blood pressure we know hypertension leads to strokes and infarcts, and low pressure is associated with shock and syncopal events. However, normal functioning for some people might be on the high end, even if in the long run, that might be harmful. Hence we assume a 'normal' blood pressure which we are aiming at, which seems to be the general state in man.
Now most medical diseases and such, work in like manner - especially Chronic ones. When an hypertensive has high blood pressure, this is usually secondary to something - an excessive sodium load or overcome renal vascular occlusion say, though often we don't actually know and term it idiopathic. For that person, it is 'normal' though, how his body's homeostasis works, but is unhealthy when measured against our concept of Health, an hypothetical ideal.
So let us review Atheism by these criteria. Clearly it is not the norm for humans, as universally all cultures have some form of religious belief historically. So already we are dealing with an outlier. Now hyper-religiosity is also used as a symptom of mental illness, but that is because it is one that is highly sensitive to being picked up - someone declares themselves a prophet or so. A hyper-atheism on this same spectrum of belief, would not have any overt symptoms beyond perhaps denying religion or maybe a lack of tolerance toward it. So its sensitivity is low as a symptom. Atheists though, are over-represented in mental health care use, and religion is protective. Numerous studies have demonstrated that religion is positively correlated with better mental, as well as physical, health. For instance:
Religion, Health, and Psychological Well-Being
Religion and health: Is there an association, is it valid, and is it causal? - ScienceDirect
Religious and Spiritual Factors in Depression: Review and Integration of the Research
Non-Religion is associated with poorer mental health outcomes. Beyond that, religious people tend to be healthier in general than their peers of the same diet, lifestyle and socio-economic class who are not. While clear causality has not been demonstrated beyond doubt, the correlation is definite, though a specific physiological mechanism for it has not been found, and psychological theories tend to cluster around ideas of 'certainty' or so, but even there, people with religious affiliation and strong devotion to their religious practices, outperform all on health parameters.
Secularity, religiosity, and health: Physical and mental health differences between atheists, agnostics, and nonaffiliated theists compared to religiously affiliated individuals - ScienceDirect
The Benefits of Religious Fundamentalism
To return to what is Healthy then, Atheism and non-religion clearly have worse ourcomes on measurable health factors and use of medical services. It is also not a natural position for humans to take, as the vast majority of humans throughout history have been religious. We are thus forced to conclude that it is an outlier on human functioning with potential factors predisposing to disease or undesirable outcomes, and our Ideal Man, our hypothetical examplar of health, would be religious.
What of Disease though? A disease is something which produces specific symptoms or a syndromic association of symptoms, that negatively affect health. It is defined by taking factors that deviate from the norm, and to cluster them together, as in my above example of Hypertension or associated sequalae like strokes. A lot hedges on definitions here, but the argument to label Atheism and Non-Religion unhealthy is strong; but are these symptoms of a presumably mental illness, or merely a predisposing malady such as being born with a less effective gene, or unhealthy human behaviour like smoking or a sedentary lifestyle? The argument to label it a disease itself can even be made, but of course, that hedges on what is termed desirable - if we cannot agree on basic desirable outcomes, then all bets are off, such can be seen with transgenderism vs gender identity disorder.
However, being religious is in general better for you. Sure, every now and then we'd have people going off the rails and declaring themself to be God or so, but in like manner, we have people with brittle bone diseases or the ilk, in which healthy exercise would be deleterious.
Encouraging Theism, and more than that, strong devotion, would be a public health benefit. Functionally, trying to advance atheism is akin to encouraging someone to take up smoking or to not have their kids vaccinated.
End Note: Nowadays it is difficult to assess these clearly, so read studies with care. For instance, a US study found the population of atheists they studied (which tends to be younger) to have better dietary practices and be more active, so consequently were 'healthier' than the more sedentary and older religious group. This is why meta-analyses and trying to correct for confounding factors are so important, on questions such as these.
Health and Well-Being Among the Non-religious: Atheists, Agnostics, and No Preference Compared with Religious Group Members
Further to note, most studies are done in the WEIRD countries (Western, Educated, Industrialised, Rich, Democratic), so the religious populations we are talking about, tend to be mostly Christian, with some Jews and Buddhists and Hindus vs the modern expansion of atheism and non-religiously affiliated, which may be a confounding factor.