The psychology of faith
The one common denominator between almost all religions is faith. One could even argue that faith plays a fundamental role in human psyche. It is arguably what has led millions to believe in certain religions and practices so vehemently.
All religious context aside, It is well-established how effective the human psyche can be. Take for example the placebo effect. The body can cure its own illnesses just through the mere fact that the mind Is convinced that the body is being cured. Faith also amplifies self-confidence so when somebody believes that a certain god is on their side they would become much more assertive and sure-footed.
This explains occurrences and practices where people with strong faith are more successful and are able to make certain things happen, like cure diseases and make others do things for them, it's all the psyche. If you believe that you are going to fail at a certain task then you are more likely to fail. And if you believe in yourself and in your abilities then you are more likely to succeed.
Not to mention coincidences that happen in the world and each explaining them in their own frame of religious context which amplifies their faith and gives positive feedback the faith system.
In general terms within the bounds of reason, why when somebody tells you “I'm going to pray for this and that” refrain from arguing against their practice of faith, and just let them pray what they want, because what that effectively does is amplify their self-confidence and optimism. However I can't but feel powerless when those same people cause themselves such large mental turmoil over belief. It goes both ways.
To sum up, I think it's important to at least understand the perspective of faith and to observe and understand how much of a strong effect and even a versatile tool it can be within any context.