I agree with what you say until the last paragraph, it’s true that Enlightment was a reaction against Church-state in some form, but at the same time, in a nuanced and philosophical form, Enlightment also developed from protestantism.
You see, with Copernicus started the Scientific Revolution and all was well (the Church was mostly ok with science except for the Galileo incident), in Universities, the complementary philosophical approach was Scholasticism, which could be adapted to the new sciences as demonstrated before by Albertus Magnus and Roger Bacon.
However, a threat to this was in some way Reformed theologians and Reformed philosophers, including scientists themselves such as Newton, who despised the Church for theological and political reason. Add to this the whole Renaissance philosophy which dumbed the image of the Medieval Church and the result is:
Secret societies. Everywhere.
From Scotland, England, Germany: Freemasons, Rosicrucians, Illuminaties. Protestant scientists and intellectuals who began to reunite and invent some obscure rituals and alchemical language, and to think in how to overthrow the Old Regime.
From them Enlightment was born. There were obviously some good values in Enlightment, but with it came also a strong anti-catholic movement. And from that came the martyrdom in the French Revolution and other wars fought for liberty, but also for secularism.