Medieval frontier wars drove large-scale migration and conversion of religious minorities in both directions.
Evidence
As Europe north of the Pyrenees confronted new heresies and sent waves of crusaders to face the Saracen infidels, Spain too faced military and religious turmoil. Wars of conquest, often motivated (or at least justified) by ideologies of crusade and jihad, pitted the Christian rulers of the north against the new Almoravid Muslim dynasty. These conflicts provoked emigration and conversion of large numbers of religious minorities: many Muslims moved south, many Christians and Jews went north into the expanding Christian kingdoms. Large religious minorities remained in the urban areas: Muslims and Jews in the newly conquered Christian towns, Christians and Jews in the Almoravid empire. Some converted to the majority religion, responding to a mix of social and economic pressure and spiritual turmoil; others clung to the faiths they had been born into. — John V. Tolan, Saracens, 796