The law regulating what the police are allowed to forbid is very limited. They can deny permission for a demonstration due to traffic disruption, but not threats of terrorism or international relations. It’s currently being debated in the Riksdag (the supreme legislative body).
Secondly, the police are in their rights to deny permission for protests/demonstrations that are clearly illegal for some reason. The legislation regulating incitement against ethnic groups (which Muslims are covered under) is fuzzy however, and this is mostly uncharted territory. Context matters for the letter of that law, in legalese the law forbids certain “verbal statements or messages” with a purpose to incite ethnic groups. But is burning the Quran a “message”? Arguably yes (imo) in this context, but it hasn’t been tried.
There was a dismissed case tried in court with a Quran burning, but the context there was different. There have also been some police reports regarding other Quran burnings that were never prosecuted, because the prosecutors only put forth cases to trial that they are convinced that they can win (this is how the system is designed).
What we are waiting for is a case that fulfills, or seems to fulfill, the letter of the incitement law with regards to context, that will be prosecuted and tried in courts all the way up to the supreme court.
The previous Quran burning might fulfill those criteria (burned Quran outside a mosque during Eid). It has been reported to the police and we are waiting to see if the case will be brought to trial.