How will not being alone affect different faiths?
There was actually some wingnut evangelical who stated that aliens could not be Christians because they were not from Adam and Eve's lineage. Apparently it has come up in their rarifed circles.
Oh, FFS!
I believe we would need incontrovertible evidence that these civilizations exist or existed. But we have incontrovertible evidence we landed on the moon and that the earth is round, and still people claim conspiracy and fake news. I think most of these people would have to meet an actual alien to be convinced they were real.
Even then it would be construed as a hoax if someone entirely trustful as Franklin Graham or Pat Robertson was to "explain" it that way...
It depends on the specific faith.
I was sparring with a young earth creationist a few years ago and made a totally incidental comment about the possibility of life on other worlds and was astounded at the virulent response I got. He went on a stem-winding tirade in which he defended the (extra-Bibilical) notion that god created life on Earth alone, and that any life we might find on other worlds would be some form of panspermia from Earth itself.
In fact they appear to be getting out in front of it with bizarre hypotheses about how the cataclysm of the Flood spewed all sorts of living material into space.
Similarly, I note that lately the same people have been doing a running commentary on scientific developments such as the recent Pluto fly-by and comet rendezvous, claiming that these findings "clearly" demonstrate, not just a young earth, but a young universe. They also have a pet theory that the organic molecules or water found on comets are, again, leftovers from the Flood (conveiently ignoring that the orbital period of many comets are so great that they are only visiting the inner solar system for the first time since the alleged Flood).
When you think about it, a 6,000 or 10,000 year old earth implies a similarly young universe, and this greatly increases the credulousness required to believe such things.
I would really hate to be on the losing end of those trends ...
I guess I do not understand how someone can suspend logic in the face of religious storytelling. I tend to believe that it is similar to children's belief in Santa Claus, the tooth fairy or the Easter bunny. They know better but fear losing something if they face up to it.