I think the most natural alliance between the two is the one against secularism. In a postmodernist world which cherishes the pursuit of pleasure and has an open disdain for the concept of higher spiritual identity, Christians and Muslims can unite under the simple banner of sacrifice of self in pursuit of treasure in the age to come. This alliance extends naturally to other fields such as the scientific.
I think the biggest issue facing this proposition is the Islamic belief, in some cases justified, that the more secular and libertine morality system in the west is a byproduct of our religious heritage.
We must be accountable to our own ethical codes and sincere in our pursuit of morality to demonstrate the transformative power of Jesus Christ’s Grace to us and how it truly helps those who follow The Way to live a better Way.