I don't feel like I have much to add about this particular instance, other than to say I am very happy to live in a country that has already litigated the "is burning sacred symbols an act of free speech, legally speaking" question and come to the conclusion of "yes."
And yet, more than half the population of said country would support legal punishment for the act of "desecrating" the national flag, and where there remains an ongoing political battle to introduce legislation to that effect. Honestly, I don't think your country is nearly as secular as you think it is.
But the problem here is "symbols," because that implies a specific religious view of sacredness, one rooted primarily in Protestantism. Protestantism entails a particular form of iconoclasm that is mostly unprecedented in religous history, most protestant denominations reject the idea that objects, in and of themselves, can be sacred outside of their ability to symbolize something sacred. For Protestants, destroying an image of Christ is not an injury to Christ himself but a political statement against what Christ represents, which is still capable of enormous offence but not the same as how the same act might be perceived in other religious traditions.
The problem of burning the Quran is not political. It's not that the person burning the Quran might dislike Islam. The problem is that the Quran is not a sacred symbol but a sacred object that has iconic properties, like a Torah scroll or a medieval Catholic relic or a Hindu idol or a mikoshi or an actual Orthodox icon. Most religions don't clearly separate the sacred and profane into separate worlds like Protestants do, and thus don't necessarily regard physical objects as purely symbolic.
This is a problem, because while it might seem that "we should be able to burn all religious symbols" is a neutral, secular stance, it's not. It's an explicit endorsement of a Protestant view of the sacred as the only "correct" form of religious belief. It essentially requires us to assume that only Protestantism entails a correct understanding of God and reality and thus all other religions need to be educated and corrected in order to resemble Protestantism.
Islam and Hindusim coexisted for centuries despite having radically incompatible beliefs about the nature of the sacred. It's not because Muslims went around burning Hindu idols and force feeding them beef to show the idol worshippers the error of their ways, it's because the reality of people with different beliefs living together requires a kind of peace treaty. The basis for a functioning multi-religious society is not "you have to accept that the things you care about don't actually matter because they don't matter to me", it's a mutual agreement to
leave each other alone.
There is a place for provocation and satire and for beliefs to be challenged, but there is also a line at which those things intrude into the sacred, and morality aside you simply cannot expect people to ever respond nicely when things they consider sacred are profaned. That's not something people will ever learn to tolerate. It's not going to happen.