Fundamentalist Christians believe Genesis literally. So that could cause a big problem, when they see that in fact stars are not 'in our sky', but just other solar systems. I'm pretty sure they reject the possibility of life on other planets, mainly because God created the chosen people here.

Interestingly, Ray Bradbury wrote a short story about the ramifications of life on other planets. Basically, the birth, ministry, death and resurrection of Jesus Christ would be an epochal event that is triggered by society reaching a certain level of accomplishment (think Golden Age in Civilization III). Jesus roams the galaxies, repeating this cycle on various planets as their societies progress to a point where they can even understand his ministry. There's a guy trying to catch up to him but always misses him, he always arrives closer and closer but always right after the ascension.

I don't think more rational Christians who take the Pentetauch as metaphorical, would have any issues along these lines.