We who have been raised in a primarily christian, agonist, atheistic society have a different concept of offensive than that of a muslim or arabic majority culture. To be offended, we need to take offense by learning to be offended at bullfeathers, or not have confidence in our own beliefs. The muslims have been taught to take offense at "pictures of mohamed", it is a learned reaction to disrespecting a bullfeathers quzi historical, fiction or mythical character. Belief in a fictional mythical character or the laws of such is a now a joke, hence, anyone who believes a fiction cannot be taken seriously. It is impossible to take seriously any belief system that is just wrong. We can see now these are just juvenile meme systems. Live this way and good will come, and if you do not, hell will come to you.
So once we see all religion as just meme systems, how can we take them seriously? Why would we ever be offended at a religions wild ideas unless we are in a religion, and trying to be living with ludicrous beliefs, aka, a big man in the sky concept.
Now should we have the right to offend them? That is there reaction to something that is acceptable in much of our society. So do we have a responsibility to clean our behavior of things that they find objectionable. It that is yes, then they also have the responsible to clean their behavior of things we find objectionable. This makes coexistence logically impossible, unless everyone learns to not be offended. How does one learn to not be offended at the pushing of bullshit onto the youth and others?
If we have confidence, we can separate out others crap beliefs out, and make a decision to ignore, avoid hearing, preach realism back, or let it all go as just their delusions or their beliefs. If you are offended, it is your problem.