Francesca Gino and Michael I. Norton suggest that there are real benefits to rituals, religious or otherwise, in Scientific American:
Recent research suggests that rituals may be more rational than they appear. Why? Because even simple rituals can be extremely effective. Rituals performed after experiencing losses – from loved ones to lotteries – do alleviate grief, and rituals performed before high-pressure tasks – like singing in public – do in fact reduce anxiety and increase people’s confidence. What’s more, rituals appear to benefit even people who claim not to believe that rituals work.
The extensive article looks at rituals from many settings: symbolic things we do “before, during, and after a meaningful event”.