That's just a rhetorical trick designed to disguise the imbalance of perception and justify tactlessly steam-rolling the feelings of others.
If I draw a picture of a cartoon cat saying "Pakis go home" on a council estate, or perhaps a bridge across a motorway, I would correctly be taken to task for offensive and threatening behaviour. If I try to defend my actions as free speech, or nothing more than a " doodle", all sane people would recognise that the former was not valid, and the latter a gross misinterpretation.
The terms "doodle" and "cartoon" technically refer to the medium by which the message is delivered. Their apparent harmlessness is not part of the medium, it is related to the inoffensive nature of the standard output in that medium, and is therefore a value judgment. If we then create a doodle that is not harmless, we can still refer to it as "doodle", but it is disingenuous to extend the general perception of this as harmless to the particular, and unusually divisive, example.
We are a moral society, and therefore have a set of moral duties towards each other. Among these is a basic civil attitude towards each other's feeling, which we should not hurt without consideration. There are times when we absolutely should say things that might cause hurt feelings, but they should be justified. To do say or do things which cause alarm and pain for no reason other than taking a delight in causing them, or just refusing to consider somebody's pain, is not valiant, or worthy of praise.
Sacrilegious cartoons are not in and of themselves important to draw, they carry no important message and do nothing to help reconcile differing world views. By refusing to consider the hurt feelings they cause, or by choosing to justify that as a failing on the part of anyone who takes offence, we demonstrate a paternalist arrogance that is corrosive to our moral authority in general and create an air of deep mistrust that makes it harder to communicate with other civilisations on a reasonable basis.