The relationships of spirituality with human social cognition, as exemplified in autism spectrum and schizophrenia spectrum cognitive variation, remain largely unstudied. We quantified non-clinical levels of autism spectrum and schizotypal spectrum traits (using the Autism Quotient and the Schizotypal Personality Questionnaire-Brief Revised) and dimensions of spirituality (using the Hardt Spirituality Questionnaire) in a large sample of undergraduate students. We tested in particular the hypothesis, based on the diametrical model of autism and psychosis, that autism should be negatively associated, and positive schizotypal traits should be positively associated, with spirituality. Our primary findings were threefold. First, in support of the diametric model, total Spirituality score was significantly negatively correlated with total Autism Quotient score, and significantly positively correlated with Positive Schizotypal traits (the Schizotypal Personality Cognitive-Perceptual subscale), as predicted. Second, these associations were driven mainly by opposite patterns regarding the Search for Meaning Spirituality subscale, which was the only subscale that was significantly negatively associated with autism, and significantly positively associated with Positive Schizotypal traits. Third, Belief in God was positively correlated with Positive Schizotypal traits, but was uncorrelated with autism traits. The opposite findings for Search for Meaning can be interpreted in the contexts of well-supported cognitive models for understanding autism in terms of weak central coherence, and understanding Positive Schizotypal traits in terms of enhanced salience.