I would elaborate a bit more, and I think you have a good analogy with “burning a cross in a black family’s yard”.
Just like burning a cross to protest the church is different from burning it in someone’s yard to threaten them, burning a Quran in the context of protesting against (for example) the Iranian regime is different from burning the same Quran while simultaneously encouraging violence towards Muslims.
I used Iran as an example because they specifically have a religious leadership that uses exactly the Quran to justify their laws.
There are plenty of non-Muslim Iranians that have burned Qurans in anti-regime protests, specifically to separate the religious regime (symbolised by the Quran in that context) from the country and its culture as a whole. That is: They are specifically protesting the religious regime, and therefore don’t burn the flag, which they don’t associate with the regime.