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

                There is no one among us who is unaware of what the Christians say defaming the Prophet (peace and blessings of Allaah be upon him), and we are not unaware either of the gheerah (protective jealousy) of the young men of the Muslim ummah towards their religion and their Prophet (peace and blessings of Allaah be upon him). Is it permissible to respond to those who defame the Prophet (peace and blessings of Allaah be upon him) by insulting the speaker, knowing that I insulted one of them and some of my relatives advised me not to do that again, because it will make them defame and mock him even more, so their sin will be on me?.
Praise be to Allah.
    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.