Most Christians have no problem getting along with non-Christians. This may seem confusing to some; after all, Christianity teaches that those who are not reconciled with God will not receive salvation. Why care about people who aren't going to Heaven?
One could say that while a particular non-Christian is alive we really don't know that that person's eternal destination won't make a course change at a later date. That's a valid observation, but not the real reason.
Christianity makes a radical claim about the relationship between believers, nonbelievers and God: we're all family
. God created the souls of all, thus he is the father of all, believers and nonbelievers alike
. All of the children have gone astray - but some have reconciled with him while others have not.
When one is faced with the earthly parallel - being in good standing with Dad while some of the other siblings aren't - one is charged with three tasks: to build and maintain the relationship with Dad, to build and maintain the relationships with the wayward siblings without doing anything that interferes with the paternal relationship
, and to act as a bridge between the wayward siblings and Dad. That third task is tricky; there will be occasions to discuss the rift outright, but most of the time it involves nothing more than being a positive influence to that sibling.
Christianity works the same way. Loving God doesn't mean giving up on non-Christian friends. We may have to reassess what kinds of "fun" we pursue with them, though. (Heck, sometimes we have to reassess the "fun" we pursue with fellow Christians.) Witnessing to nonbelievers isn't all Amway sales presentations. Most of the time it's just bringing good to someone's life.
The hardest part of doing good to others is when it requres criticism. We see them doing something destructive, and we want to help. We need to effectively communicate what the problem is, how it hurts that person, and how the future can be better when that problem is dealth with.
Most Christians grasp all this, even if they haven't thought it out as thoroughly as outlined here. They care about both believers and nonbelievers out of the same human motivations that drive us all, and because they believe in a God who values everyone.