How Must Muslims React to Disrespect and Insults against the Quran and the Prophet Muhammad?
There were insults and disrespect against the Quran and the Nabi/Prophet in olden times (al-Anbiya  36-41) and they will still be there in the future. The Quran teaches Muslims very clearly how to behave in such difficult situations.
Even though the tradition determines physical violent actions against disrespect and insults, the Quran doesn’t approve of such behaviour. The Quran allows only the following reaction and behaviour:
“…and you shall hear from those who were given the Book before you, and from those who are idolaters, much hurt; but if you are patient and Godfearing — surely that is true constancy.” (Al Imran  186).
Don’t pay attention to the bullying’s
“…and when the ignorant address them, they say, “Peace!”…” (al-Furqan  63. Also al-Araf  199; al-Qasas  55).
Retaliate evil with favour
“And not equal are the good deed and the bad. Repel [evil] by that [deed] which is better. You will certainly find that your enemies will become your intimate friends.” (Fussilat  34. Also al-Anam  107-108).
Advice and argue/debate with Hikmah (wisdom) and the Quran
“Invite (all) to the Way of thy Lord with wisdom and beautiful preaching; and argue with them in ways that are best and most gracious…” (an-Nahl  125. Also al-Anam  70; an-Nisa  148).
Stand up and go/turn away
“…when you hear the verses of Allah [recited], they are denied [by them] and ridiculed; so do not sit with them until they enter into another conversation…” (an-Nisa  140. Also al-Araf  199; al-Anam  68).
Note: The verses about Fitnah in al-Anfal  39 and al-Baqara  193 deal only with difficult tests during the combats in war. They have no interest except for war. Even so the punishment of the munafiqun (hyprocrites) in Tawba  66 is related to the afterlife, according to the context. It’s about the punishment from Allah in the hereafter, not the punishment to humans.