Coexist. Doesn't that sound nice? And it would be nice, if it just meant coexisting with others without killing them or otherwise causing them harm. But that isn't really what people mean by it.
What Ayn Rand and Christianity have in common is that reality exists, and we humans can know and understand that reality. They differ in what that reality is, but the fact that there is a knowable reality makes Christians and objectivists closer in thought to each other than with the postmoderistic world. Postmodernism had been described by Josh McDowell and Bob Hostetler as “A worldview characterized by the belief that truth doesn’t exist in any objective sense but is created rather than discovered.”
The problem with this Coexist meme is that it's saying all religions are equally valid. You run into logical fallicies that way, since the various religions contradict each other. They can't all be true. What it amount to is a denial of truth. It is the quintessence of postmodern thought. "Oh, that's just what they believe" so it's OK, we can't question it. In other words, it has no connection with reality, no one can know truth.
So should Christians live toghether with other religions without kiling them or harming them in some way. You betcha. Should we avoid offending their beliefs? No, we should speak the truth.