Please do not confuse and equate "freedom of speech" with hate speech.
There are many secular democracies in the world where desecration of religious symbols (like burning holy books) is a crime. In fact, Sweden too is currently debating whether it needs to re-examine its laws and bring similar laws to counter such hate speech:
Sweden's justice minister has said his government may be open to amending a protest law, after the public burning of a Quran in Stockholm last month sparked fury across the Muslim world.
In fact, Swedish police have even charged some of these "protestors" for burning the Quran under hate crimes laws:
Sweden’s hate speech law prohibits incitement against groups of people based on race, ethnicity, religion, sexual orientation or gender identity. Some say burning the Quran constitutes incitement against Muslims and should be considered hate speech ... Seeking guidance from the justice system, Swedish police have filed preliminary hate crime charges against the man who burned the Quran outside a mosque in Stockholm in June and desecrated Islam’s holy book again on Thursday. - Euronews, 22 July 2023
Yes, criticism of any religion should be allowed and even welcomed. Islam is no exception to this, and since its birth has experienced it - even Islamic scholars who wrote Prophet Muhammed (pbuh) early biographies have included criticism directed against him, and their own critical views of him and Islam. But let's be clear that burning the Quran to "criticise" Islam isn't a rational argument for anything - it is just hate politics to provoke enmity between the muslim community and the others.
So your question really is - what is the liberal Islamic way to deal with hate speech from non-muslims?
The best answer to that is in the conduct of Prophet Muhammed's (pbuh) himself. When he first revealed the Quran to his community, the Quraish's mocked him and ridiculed him. He responded to these criticism with dignity and respect. As Islam grew slowly under him, and he gained more and more followers, their mockery turned to anger and even hatred. And they started to attack him and his fellow muslims, many of whom were even tortured by the non-muslims:
His life was a jihad: as we shall see, this word does not mean “holy war,” it means “struggle.” Muhammad literally sweated with the effort to bring peace to war-torn Arabia ... His life was a tireless campaign against greed, injustice, and arrogance. He realized that Arabia was at a turning point and that the old way of thinking would no longer suffice, so he wore himself out in the creative effort to evolve an entirely new solution. ...
Muhammad was not trying to impose religious orthodoxy - he was not much interested in metaphysics — but to change people's hearts and minds ... This was a frightening period. The incessant wars between Persia and Byzantium seemed to herald the end of the old world order, and even within Arabia, tribal warfare had reached chronic proportions. During the last twenty years, the ghazu, which had traditionally been short and sharp, had escalated into long, drawn out military campaigns as a result of unprecedented drought and famine. There was an apocalyptic sense of impending catastrophe. Muhammad was convinced that unless the Quraysh reformed their attitudes and behavior, they too would fall prey to the anarchy that threatened to engulf the world.
... The chief vice of the kafirun was jahiliyyah ... although the root JHL has some connotations of “ignorance,” its primary meaning is “irascibility”: an acute sensitivity to honor and prestige; arrogance, excess, and above all, a chronic tendency to violence and retaliation. Jahili people were too proud to make the surrender of Islam; why should a karim moderate his behavior and act like a slave (abd), praying with his nose on the ground and treating the base-born like equals? ...
Instead of succumbing to the jahili spirit, the Qur’an urges Muslims to behave with hilm, a traditional Arab virtue. Men and women of hilm were forbearing, patient, and merciful. They could control their anger and remain calm in the most difficult circumstances instead of exploding with rage; they were slow to retaliate; they did not hit back when they suffered injury, but left revenge to Allah. Hilm also inspired positive action: if they practiced hilm, Muslims would look after the weak and disadvantaged, liberate their slaves, counsel each other to patience and compassion, and feed the destitute, even when they were hungry themselves. Muslims must always behave with consummate gentleness and courtesy. They were men and women of peace: "For true servants of the Most Gracious are they who walk gently on the earth, and who, whenever the jahilun address them, reply 'Peace' (Salam!)"
... After the affair of the “satanic verses,” the conflict with the kafirun became very nasty. Abu Jahl regularly subjected any Muslims he met to vitriolic verbal abuse and slandered them with vicious lies and rumor; he threatened merchants with ruin, and simply beat up the “weaker” Muslims ... It must have been very difficult indeed for the Muslims, brought up in the jahili spirit, to practice hilm and turn the other cheek. Even Muhammad sometimes had to struggle to maintain his composure. - Muhammad: A Biography of the Prophet by Karen Armstrong
Does the Quran support that muslims should behave with hilm?
As the background of Surah Fussilat highlights, the question that was vexing the Holy Prophet at that time was as to how be should carve out a way of preaching his message when he had to face such heavy odds on every side. The solution he was given to this question was: "Although apparently the obstacles seem to be insurmountable, the weapon of good morals and character can smash and melt them away. Use this weapon patiently, and whenever Satan provokes you and incites you to use some other device, seek refuge in Allah."
And who is better in speech than he who [says: "My Lord is Allâh (believes in His Oneness)," and then stands firm (acts upon His Order), and] invites (men) to Allâh’s (Islâmic Monotheism), and does righteous deeds, and says: "I am one of the Muslims." - 41:33
The good deed and the evil deed cannot be equal. Repel (the evil) with one which is better (i.e. Allâh orders the faithful believers to be patient at the time of anger,6 and to excuse those who treat them badly) then verily he, between whom and you there was enmity, (will become) as though he was a close friend. - 41:34
But none is granted it (the above quality) except those who are patient - and none is granted it except the owner of the great portion (of happiness in the Hereafter i.e. Paradise and of a high moral character) in this world. - 41:35
There are many other verses in the Quran that outline how muslims should deal with non-muslims who seek confrontation with them:
So if they dispute with you (Muhammad صلى الله عليه وسلم) say: "I have submitted myself to Allâh (in Islâm), and (so have) those who follow me." And say to those who were given the Scripture (Jews and Christians) and to those who are illiterates (Arab pagans): "Do you (also) submit yourselves (to Allâh in Islâm)?" If they do, they are rightly guided; but if they turn away, your duty is only to convey the Message; and Allâh is All-Seer of (His) slaves. - 3:20
O you who believe! Stand out firmly for Allâh as just witnesses; and let not the enmity and hatred of others make you avoid justice. Be just: that is nearer to piety; and fear Allâh. Verily, Allâh is Well-Acquainted with what you do. - 5:8
The above verses clearly state that Muslims need to treat non-Muslims justly and honourably. Prophet Muhammad (pbuh) always emphasised that a muslim should always be mindful of his manners and etiquette when dealing with others even in the face of hostility.
(I know there are many Hadiths highlighting how the Prophet behaved with genuine respect, generosity and frank honesty in dealing with non-muslims. And all muslims are expected to emulate him - but citing them all would make this answer even more tediously long ...)