I was raised a Catholic as a child so "witchcraft and magic" is something I experienced during the Sunday masses or service. During the Eurcharist, the invocative ritual of the priest culminate in what they call as the consecration where the bread is transformed into the body of their deity. This magical process is called "trans-substantiation". Is it effective? To many, it is still wafer after that; but to others, their consciousness are so altered after the communion that it resulted in healing, behaviorial change, temporary consciousness high, etc.. In Wicca, same thing happens replacing the male deity with a feminine one, and the priestess does the drawing down the moon ritual. Probably, everything is subjective.
But if you refer to witchcraft not as a religion but as a technique, catholicism did have a practice called "novena" directed to the deity or some saints to achieve material gains.
From these you can see the parallelism. I believe it is just a matter of temperament as to what belief system (including positivism/empiricism) a person is drawn to or have affinity with. In the end, all of them can lead to dogmatism