Let us briefly consider world religions with respect to mental health, starting from the polytheistic going to the monotheistic to consider the two criteria for growth viz. (1) dependence on God (2) serving humanity.
First let us consider polytheistic religions, starting with animistic tribal religions with emphasis of worship of objects. Their focus is on worshipping several deities and they serve a small segment of humanity. Then we have traditions like Hinduism in which its followers worship statues as well as so many other creations but when we ask the priests class they assert that there is only one God (Bhrama). So their elite class just worships one God, while the rest worship several.
We can then consider Abrahamic faiths like Judaism, Christianity, and Islam which are supposedly monotheistic. Nevertheless, if we consider Christianity and its various denominations it has become a shade of polytheistic due to introduction of concepts such as the Trinity, by people like Paul, 300 years after the death of Jesus (AS).
When we consider Judaism it seems monotheistic indeed, whereby Jews worship one God, but it is a tribal religion exclusive for themselves which the gentiles cannot have any claim over. So there is no conversion into Judaism. One needs to be born of a Jewish mother to enter the faith, which has very different ways of looking at people who do not believe in the faith. So its domain of sincere public service is limited to its coreligionists.
When we consider Islam, the last of the revealed religions for ALL humanity (the greatest domain of service) to the last Messenger of God, Muhammad (SWAS) and it is not parorchial as other faith. It is practiced by the whole diversity of mankind and it enjoins true monotheism -- the strict worship of just ONE God. It does not compromise on that. In fact, tawheed, or belief in ONE God, is its principal pillar.
We have seen that out of all world religions that we have considered, practicing Islam sincerely has the most significant effect on the growth of the soul ie improvement of mental health. Thus, Islam is the best way of life (not just a religion) to improve our mental state.