One commonly held notion is that secularism is basically a non-religious idea invented in the 20th century.
Not so. It has deep roots. Into the Middle Ages:
As for the case of secularity, its advocates specifically want, or pretend to, ignore that it appeared in the Middle Ages, a period that was emphatically not secularist. The dividing line drawn between the Church and the State is a Christian invention that began among the Church Fathers, as a reaction against Constantine’s claim to control the Church and further culminated in medieval times. Moreover, this line was drawn by the Church, not by the State. The Holy See’s constant policy from the Investiture Controversy in the late 11th century consisted in sending the State (i.e. the Emperor or the Kings) back to its own merely this worldly—“secular” if you want—task: enforcing peace, justice, good social order. The State, on the other hand, was not merely “secular”, but claimed its share in sacrality. Just think of the adjective: “Holy Roman Empire”. Secularity was a conquest of the Church.
The idea that Catholics are working towards a form of theocracy is false.
What secularists do not accept is Catholics working according to their values.
A democratic society cannot require people, including politicians, to stop acting on their religious values in the public square.