Some say only the world's largest religion, Christianity, might run into problems in the face of alien intelligence. The Bible says humans are made in the image of God, who cherished his creatures so much that he sent his son Jesus to Earth to save humanity from sin. People are therefore God's favorites, made in his form and promised salvation through Jesus. He didn't come to save the great apes, for example, and he certainly didn't come to save little green men. So this is a unique relationship between God and man.
Many Christian scholars say no.
Still, some Christian sects would have a hard time sharing the creator. They include churches that teach a literal interpretation of the Bible, and claim Earth is the only inhabited world in the universe. At the very least, their teachings would be startled by the discovery of aliens. At the most, the churches would lose followers. Though the discovery would require some major adjustments right at the heart of theology.