It is essential to respond to those who defame the Prophet (peace and blessings of Allaah be upon him)

Defaming the Prophet (peace and blessings of Allaah be upon him) is a kind of kufr. If that is done by a Muslim then it is apostasy on his part, and the authorities have to defend the cause of Allaah and His Messenger (peace and blessings of Allaah be upon him) by executing the one who defamed him. If the one who defamed him repents openly and is sincere, that will benefit him before Allaah, although his repentance does not waive the punishment for defaming the Prophet (peace and blessings of Allaah be upon him), which is execution. 

If the person who defames him is a non-Muslim living under a treaty with the Muslim state, then this is a violation of the treaty and he must be executed, but that should be left to the authorities. If a Muslim hears a Christian or anyone else defaming the Prophet (peace and blessings of Allaah be upon him) he has to denounce him in strong terms. It is permissible to insult that person because he is the one who started it. How can we not stand up the Prophet (peace and blessings of Allaah be upon him)? It is also obligatory to report him to the authorities who can carry out the punishment on him. If there is no one who can carry out the hadd punishment of Allaah and stand up for the Messenger (peace and blessings of Allaah be upon him) then the Muslim has to do whatever he can, so long as that will not lead to further mischief and harm against other people. But if a Muslim hears a kaafir defaming the Prophet (peace and blessings of Allaah be upon him) and he keeps quiet and does not respond for fear that this person may then defame him even more, this is mistaken thinking. With regard to the verse (interpretation of the meaning): 

“And insult not those whom they (disbelievers) worship besides Allaah, lest they insult Allaah wrongfully without knowledge”

[al-An’aam 6:108], 

this does not apply in cases where they defame Allaah and His Messenger (peace and blessings of Allaah be upon him) first. Rather what is meant is that it is forbidden to insult the gods of the mushrikeen first, lest they insult Allaah out of ignorance and enmity on their part. But if they insult Allaah and His Messenger (peace and blessings of Allaah be upon him) first, then we must respond and punish them so as deter them from their kufr and enmity. If we leave the kuffaar and atheists to say whatever they want without denouncing it or punishing them, great mischief will result, which is something that these kuffaar love. No attention should be paid to the one who says that insulting or responding to insults will make him more stubborn. The Muslim has to have a sense of protective jealousy and get angry for the sake of Allaah and His Messenger (peace and blessings of Allaah be upon him). Whoever hears the Prophet (peace and blessings of Allaah be upon him) being insulted and does not feel any protective jealousy or get angry is not a true believer – we seek refuge with Allaah from humility, kufr and obeying the Shaytaan. 

And Allaah knows best.