Insha'Allah it's important to remain steadfast to the deen of Islam and the teachings of the Prophet Muhammad sulla Allahu aleihi wa salaam.
If he, sulla Allahu aleihi wa salaam, can withstand garbage being left on his door step, refuse being thrown at him, and direct insults from the jahiliyaah of his time, sulla Allahu aleihi wa salaam, insha'Allah we need to follow that example, swallow our indignation as much as possible, and follow in the footsteps of the one who was sent to perfect good character.
We absolutely have a right to feel the indignation and fury towards blatant disrespect and dishonour of our most dearly beloved Prophet sulla Allahu aleihi wa salaam - but, in my opinion, not at the cost of our deen, or our iman.
Never forget the power of Dua - especially from those who are oppressed. Consider making dua for the offenders that they be rightly guided. If Allah swt knows, in His Utimately Supreme Knowledge, that they are not from amongst those who will be guided, perhaps consider asking Allah swt to remove the challenge of their fitnah from our lives.
This dunya is a test for the believers;
al Ankaboot 29:2 - "Do the people think that they will be left to say, "We believe" and they will not be tried?
Ali 'Imran 3:142 - "Or do you think that you will enter Paradise while Allah has not yet made evident those of you who fight in His cause and made evident those who are steadfast?
wAllahu alem