I'm no language expert, but I don't think there was any "switch". As Wikipedia says, "[rite of passage] is the Anglicisation of rite de passage, a French term

I'm no language expert, but I don't think there was any "switch". As Wikipedia says, "[rite of passage] is the Anglicisation of rite de passage, a French term innovated by the ethnographer Arnold van Gennep in his work Les rites de passage." "Right of passage" may mean something similar to "right of way", and may be used my mistake when people mean "rite of passage" but there was never a switch in how "rite" is spelled.