I am afraid they do not. Every country limits freedom of speech by laws to protect the sensibilities of an individual or a group for belonging or not belonging to an ethnic group, religion, sex or sexual orientation.
For example, let us see how, France, one of the oldest, liberal democracies reacted when it found itself bewildered between the core principles of essential liberties that it was constitutionally founded upon and the strange new challenges it faced. There might be some strange lessons we can borrow from the French, before we radically turn towards a militant version of liberalism where everybody has the right to speak/write/show anything.
In 1881, the French came up with a legal framework (Loi sur la liberté de la presse du 29 juillet 1881) to regulate the publications and advertisement in public places. Right after WW II, this law came with some significant amendments. Articles were introduced by which anyone inciting others to discriminate or insult an individual or a group on the basis of religion, ethnicity, sex or sexual orientation became subjected to rigorous imprisonment with/without fine. The French, after the WW II felt it utterly necessary to come up with a stringent law that would protect the battered sentiments of a community who became on the verge of extinct by a fanatical maniac, whose brilliant orations were full of racial contempt and provocations against the community. Those orations enjoyed full freedom of speech, intoxicated an entire nation and rest we all are aware of.
The French, in defiance to their quest for modernity and individual liberty banned a number of films which were deemed to be impertinent to Christianity. Newspaper articles faced challenges in court and later lost for condemning the Catholic Church for abetting the realization of Auschwitz. Ultimately, he had to appeal to European court of human rights and prove himself innocent.Very recently and quite ironically, Dieudonné M’bala M’bala, the stand up comedian was arrested for merely sympathizing with a terrorist on Facebook. People argued, if Charlie Hedbo enjoyed its own freedom of speech, what error M’bala had commit?
If France was right in allowing Charlie Hedbo to publish provocative cartoons, it is more wrong in arresting M’bala. If they are right in arresting a terrorist sympathizer, they were wrong in giving Hedbo a free hand. It means, democracies, much older and mature than ours too are struggling these days to find a convenient answer i.e. liberalism must be the fundamental principle of a civilized society but to what extent? I am afraid, your previous assertion to let the society correct itself has not been taken up the western democracies. They are equally perplexed, as we are.