How should Christians interact with Muslims?

On Sunday night, we had an event (anyone on Twitter will have seen the hashtag #garlandshooting) just a few miles from our house, and it’s made me think a bit ever since.
In brief, a group held a contest for people to submit caricatures of Muhammad. Images of any kind (and especially caricatures) are bitterly offensive to Muslims. The group went so far as to offer a cash prize for the best image. As the event was winding down, two radical Muslims (who had traveled from another state) pulled up in a car, got out, and began shooting at the security guards. Police (who were on hand protecting the event) returned fire and killed both men. There was some fear of explosives.
Since the end of the event, there has been quite a lot of social media chatter about it. People often say stupid things, it’s true. One of the themes of the questions, however, is: who’s to blame?
On the one hand, the group was very provocative. They labeled it a “free speech event” and insisted they had the right to “disagree with Islam.” And in America, yes, they do. Still, they didn’t hold a plenary forum to discuss theological disagreements. They offered a $10,000 cash prize for the person who could make the “best” insulting drawing of the religious ‘father’ of all Muslims.
On the other hand, people must be held accountable for violence, regardless of how provoked they are. The two radicals believed that caricatures should be met with the extreme response of execution. They must certainly be held accountable for their actions (and, obviously, were).
What should the Christian response to this type of thing be?
More particularly, how should Christians engage Muslims? Is this a valid way?
Let us separate this idea from the idea of free speech. I certainly believe in free speech, and believe that people should have the right to lampoon, to caricature, to point out the faults, to find various and creative ways to “speak truth to power.” Otherwise, power runs amok.
But some have suggested that Christians should be involved in such events as part of “standing up for our rights” as Christians. That it’s a very short hop from outlawing one aspect of free speech (caricatures) to outlawing all aspects of free speech, and that Christians would no longer have the right to “disagree” with Muslims.
Here is where we begin to verge on equating “disagreeing with Muslims” with “evangelizing Muslims.” We begin to think that if we can’t point out everything wrong about Islam and “defend Christianity” (e.g. argue for why it is right), that somehow we have lost our one and only ability to spread the Good News with Muslims.
It’s one thing to “stand up for our rights” as Americans. But Christians must take a different approach as Christians. Is “standing up for our rights” a Kingdom principle? Would we ever do this as a citizen of God’s Kingdom?
When I read 1 Corinthians 13, I see:

Love is patient,
Love is kind.
Love is not jealous or boastful or proud or rude.
It does not demand its own way.
It is not irritable, and it keeps no record of being wronged.
It does not rejoice about injustice,
but rejoices whenever the truth wins out.
Love never gives up,
never loses faith,
is always hopeful,
and endures through every circumstance.

Here’s another thing, from Paul as well, writing to the Romans (ch 12):

Don’t just pretend to love others. Really love them. Hate what is wrong. Hold tightly to what is good. Love each other with genuine affection, and take delight in honoring each other. Never be lazy, but work hard and serve the Lord enthusiastically. Rejoice in our confident hope. Be patient in trouble, and keep on praying. When God’s people are in need, be ready to help them. Always be eager to practice hospitality.
Bless those who persecute you. Don’t curse them; pray that God will bless them. Be happy with those who are happy, and weep with those who weep. Live in harmony with each other. Don’t be too proud to enjoy the company of ordinary people. And don’t think you know it all!
Never pay back evil with more evil. Do things in such a way that everyone can see you are honorable. Do all that you can to live in peace with everyone.
Dear friends, never take revenge. Leave that to the righteous anger of God. For the Scriptures say,

“I will take revenge;
    I will pay them back,”
    says the Lord.

Instead, 

“If your enemies are hungry, feed them.
    If they are thirsty, give them something to drink.
In doing this, you will heap
    burning coals of shame on their heads.”

Don’t let evil conquer you, but conquer evil by doing good.

So, if we’re thinking about participating in these kinds of events, let’s just ask: do they line up with 1 Corinthians 13, and Romans 12? As Americans, we have to worry about our rights, because they might be legally dripped away. As citizens of the Kingdom, we don’t have to worry about our rights, because God never changes toward us. Thus our response can be different. We can let God take care of the justice, and instead we do what He commands us, which is largely to be an ambassador of good news, of mercy, of healing, of reconciliation, of hope.

Are these kinds of events the kind that honor Christ? Would a Muslim hearing about this event, or entering this event, or being told about this event, ‘smell’ the sweet aroma of Christ? Would they be drawn to Christ as a result of this? (“And I, if I be lifted up, will draw all men unto me.”) Would they be interested in following Christ?

If not… then is our motive Christ… or ourselves?