I stumbled upon an interesting survey conducted in 2008 called The Peters ETI Religious Crisis Survey. It examined the following:
Would either the Christian religion or selected non-Christian religions confront a crisis or even collapse when confronted with confirmation that extraterrestrial intelligent life (ETIL) exists?
According to the survey authors, they identified three questions as most important.
1. Official confirmation of the discovery of a civilization of intelligent beings living on another planet would so undercut my beliefs that my beliefs would face a crisis. 80%+ disagreed or strongly disagreed that their personal beliefs would be affected.
2. The next question asked whether the respondents particular religious tradition would be "undercut" so that it "would face a crisis." Again, the vast majority disagreed or strongly disagreed, although there was more variety among different religious groups. For example, about 95% of Mormons disagreed but only about 68% of Catholics, indicating that more Catholics think finding an alien civilization would pose a religious problem than do Mormons. Mormons are fine with aliens.
3. The last of the three focus questions asked whether religious traditions in general would experience a crisis. Many more people agreed with this proposition.
The main report in pdf format can be found here.
This survey is pretty revealing. Most religious people dismiss the idea that the discovery of an alien civilization would pose a problem for their own religious beliefs or those of the religious tradition they belong to. But they aren't sure when it comes to religions in general. In other words, they tend to look at things much more rationally when their own personal beliefs are not in question.
The discovery of an alien civilization on another planet would likely be a world-changing event. Depending on the circumstances, and all sorts of variables, it is almost a certainty that such an event would pose religious difficulties. The confidence that people displayed in the stability of their own religious belief systems seems based on little more than blind faith.