The sense here is that liberalism was a default value to which Europeans would revert once Christianity was crippled. I wonder, though, if this is anachronistic: looking at historical events with modern eyes.
Throughout history governments and usurpers sought to imprint upon their societies ideologies which reinforced their power:
In primitive groups the sense of "groupness" comes "mechanically" (instinctively) from ties of blood and kinship. In State level societies, however, people are very heterogenous, that is, they are not unified on kinship, cultural or economic grounds. The ruling class is professional and outside the obligations of kinship and has great coercive powers. Loyalty to such a system must be produced by a legitimating ideology (e.g. divine right of Kings, special relationship to Gods etc).... While coercion may sustain order, it is costly and, in the final analysis, ineffective. Ideology that establishes "moral validity is a less costly and more effective approach".
In Japan emperors claimed to be direct descendents of the sun goddess, starting with the legendary Emperor Jimmu:
And later Japanese shoguns claimed legitimacy by retaining these emperors as symbolic leaders, even while robbing them of any real political power.
Rulers of Christian kingdoms sought to likewise place themselves between God and the people. The Byzantine Empire absorbed the Orthodox Church completely, uniting church and state into a single autocracy. Byzantine artists depicted emperors being crowned by Christ himself, while lavish processions and parades took place on Christian feast days. From Norman Davies's Europe: A History:
Imperial acclamations were accompanied by the chanting of Biblical texts and political slogans.... The Imperial Profectio or 'departure', especially for battle, was marked by the distribution of alms, by the veneration of the Standard of the True Cross, and by the consecration of the army and the fleet.
In the west, Catholic Crusaders were given Papal blessings to fight Muslims in Spain and the Middle East, Pagans in Lithuania and Christian Cathar 'heretics' in France, while internal inquisitions and witch-burnings kept dissidence down. Kings and queens tried to use Christianity to legitimise their rule: the Christian cross crept onto flags in Switzerland, Britain, Norway and Sweden.
But these stamps of Christian authority used by medieval leaders were mixed with pre-Christian or secular symbolism. The Russians named their kings 'czar', the Germans 'kaiser' - both deriving from the Roman Caesar. Rome's imperial eagle would make it to flags around Europe from Albania to Austria. The Orthodox Emperors of Byzantium were raised on a shield during coronation, a tradition started by the Roman Emperor Julian, who copied not from Christ but from Germanic Pagans.
So blaming all of this repression on religion seems unfair. We are looking at a period where almost everyone would have been religious, and all natural phenomena were understood in religious terms. Religion and political ideology were indivisible. If religions were the only ideologies, and powers were always striving to stamp convenient ideologies onto populations, then religious repression was inevitable. This conflict and oppression was not necessarily caused by religion, it was caused by the illiberal norms of the day. Rulers didn't want their people to be free, they wanted them to be obedient.
In the 20th century secular communist and fascist governments did the same thing, brutally supressing free speech and seeking to control society by diverting all creative energy into the promotion of political ideology.Chinese artists were forced to paint stirring scenes of industrious peasants, Soviet composers had to write pounding military beats to encourage the revolutionary spirit.
That is: the illiberal spirit often blamed on religion thrived in anti-religious societies too.
Perhaps the important thing here is really the development of liberalism, not the decline of religion. Supposing religion had collapsed in medieval times and been replaced by atheism. Would medieval kings and queens have tolerated radical political and philosophical dissent? I have difficulty imagining it. Without the consensus of modern liberalism, some other absolutist ideology would have taken the place of Christianity.
The founders of European liberalism were, after all, religious. John Locke, sometimes called the Father of Liberalism, was a devoted Christian. In The Reasonableness of Christianity, as Delivered in the Scriptures Locke wrote:
The evidence of our Saviour's mission from heaven is so great, in the multitude of miracles he did before all sorts of people, that what he delivered cannot but be received as the oracles of God.... the works of nature, in every part of them, sufficiently evidence a deity.
If one of the great liberal thinkers could also be a great religious believer, attacks by modern liberals on religion seem misguided. Religion can be liberal. Atheist ideologies can be illiberal. Do not fight against religion, so, fight for liberty.