To be clear, I think we both agree that there is a lot of nuance and grey area in these kinds of questions, and I think it's really just a matter of where we think the lines ought to be, which is a very hard question given the lack of any clear objective standards here. I might say that a swastika is a very clear expression of support for the idea that large swaths of society should be systematically murdered, and that's more than sufficiently past a line of permissiveness. Surely burning a swastika and any other expression of strong disagreement with literal Nazism should be completely protected.
At the same time, as a gay man, Islamist ideals represent a very direct threat to my own ability to safely exist in society. Should I not be able to express my disapproval of that? If I can, in what ways exactly should I be allowed to, where is the line I cannot cross, and why is there precisely? The Muslim Brotherhood, for instance, is an explicitly Islamist party with very specific policy goals. Its flag also features a Qur'an on it. If Muslims were to be grievously offended by its burning, should it thus be illegal for me to burn the flag of an organization that explicitly advocates my own murder? The Qur'an itself (not to mention the Bible) similarly advocates for my own personal harm. You mention "certain protected groups of people" in your comment; are LGBT not included in that? Do we not get to stand up against ideals that advocate for our own destruction?
I should add that I've spent a significant amount of time in Arab countries, speak Arabic myself, and have had many wonderful experiences with Muslims around the world. I actually made an indefinite move to Jordan after university, and while I didn't wind up being able to stick around, it was an excellent time, I always felt very welcomed and safe, and just generally speaking, I have a very warm and positive impression of Muslims. I'm very much not actually advocating for these kinds of protests, and I think the people who do them are being deliberately inciteful bigoted idiots. My only point here is that these kinds of question are very complicated, and to that end, I'm not personally super comfortable with the government unilaterally deciding what the answers to them are.
I also want to make it expliticly clear that I am very aware of how various Islamophobic groups try to use homophobia in Muslims as a wedge to try to advocate against immigration, multculturalism, and as proof that Muslims are somehow incompatible with western society, which is always amusing to see given that the people who do this are almost universally homophobic social conservatives themselves. I'm strongly against that as well.