Absolutely.
Here's my idle thoughts, more broadly: I'm not a Muslim. I'm very wary of a breakdown in empathy towards Muslims. There's 1.5 billion of them on our planet, and any outcome other than figuring out how to continue to live together on it seems bleak and undesirable. It's easier to have a dialog with someone (even to the point of changing their minds) if you can be bothered to think a little about how their upbringing and the parameters of their situation affect them, and how those find expression in their lives - what drives their decisions, how they wind up ranking and navigating the same basic human desires we share.
Putting that cartoon on Google's homepage, to me, would be giving up on that, being lazy and picking sides. It's admitting defeat by deciding the world is simpler to act in if we don't bother to understand it.
It also makes it harder for people in bridging positions to function as a channel for this dialog. The bilinguals, the overseas students, that interact with friends and family, that try to explain but end up having to justify cold shoulders.
Check out some indie student music from Arabic countries some time. There's some on YouTube with English translations. Notice all the grappling with their own religion they do, or with gender roles in their society. These aren't dumb, unaware people.
Heck, they're even capable and appreciative of good satire.
But I guess people will always look to the easy and emotional options. Which explains a lot of the 'how' in the 'how we got to this point' question - on both sides.
Yet it protects your rights to have bad manners.