Not only were science and religion compatible, they were inseparable-the rise of science was achieved by deeply religious Christian scholars.
Because God is perfect, his handiwork functions in accord with immutable principles. By the full use of our God-given powers of reason and observation, it ought to be possible to discover these principles.
These were the crucial ideas that explain why science arose in Christian Europe and no where else.
Slavery ended in medieval Europe only because the church extended its sacraments to all slaves and then managed to impose a ban on the enslavement of Christians (and of Jews). Within the context of medieval Europe, that prohibition was effectively a rule of universal abolition.