Most religions are rational per se. However, some of them, such as mystic pagan religions, idol cults and modern cults, are irrational because of lacking a comprehensive religious text.
However, most of time, religion in practice is often irrational. Because religions can't compete its rationality with other knowledges, such as natural science (place doubt on religious claims), psychology (which often reveals plots of religions), history, social and political science (which often reveals the function of religions). Due to those vulnerability, religions in modern world acts as a soothe of mental wounds, rather than a rational explanation, observation and solution of things.