A crucifix is a cross with a representation of Jesus’ body on it.
Jonathan is a member of the Protestant Church of England, a form of Christianity that broke away from Catholicism, rejecting some of its practices. They saw the extreme importance placed on ritual and holy objects to be idolatrous and therefore sinful. The woman who hands Jonathan the crucifix is of the Eastern Orthodox Christian faith. Eastern Orthodox worship also involves much ritual and displays of piety, as well as a great emphasis on the use of icons. To Jonathan, putting such importance onto an object such as a crucifix might have seemed sinful, as it diverts worship away from God to a mere symbol instead.