The anthropic principal becomes less compelling; to say nothing of the religious implications.
Religion will last for a very long time into the future, forget about major lasting change on that front other than some rearguard action to ensure survival.
Some people think Christians would have a hard time with extra-Terran life because the Bible doesn't mention any life other than the life here, and therefore any such life would arguably be free from the weight of Original Sin, yada yada yada. But I'm pretty sure if life on another planet was discovered (even intelligent life) they would just reinterpret the Biblical references that seem to refer to "Earth" as referring to "The Universe" and make "The Garden of Eden" a metaphor, and the flaming sword would become a supernova, blah, etc., yada, blah, blah, blah. At the end of the day, approximately 0.0% of Christians would say "Hmm... the Bible is obviously incomplete and or inaccurate, so maybe the whole thing is a load of bollocks" or whatever. And I expect it would be about the same for every other faith.