Most religions focus on prophetic revelations which are given specifically to humankind. In the biblical creation story, Mankind is a reflection of God's image, and man is the highest form of life, given lordship over all other beings. The Koran also has many passages which seem to award man dominion over creation.
If there are other intelligent life forms, especially if they are more advanced than humans, scripture it calls scripture into question. Religions like Christianity, Judaism, and Islam argue that God reveals himself through events in human history. Suppose there are many worlds with many civilizations, we may ask the question why God would choose to act specifically on our planet and why he speaks to humans in particular.
Many religions are vulnerable to some version of this scrutiny. Why would Jesus only save human beings? Why is Mecca so important to Islam if the earth is one of millions of worlds?
Unless aliens have identical religious stories to us, religious myths will appear to be cultural constructs, which privilege human beings out of ignorance, not revelation. In the Christian tradition, Christ died to save mankind specifically. Other worlds would have to have their own version of the crucifixion to seem credible.
Even if religions attempt to shoehorn aliens into their dogma, their credibility will be irreparably damaged because mankind will no longer seem special. Earthly religions focus on humans, and the discovery of new species will take the spotlight from them.