Non-abrahamic religions like Hinduism,Jainism, Buddhism, believes in existence of world systems other than current one.
Buddhism is especially is accommodative in terms of acceptance, of evidences that refutes Buddhist world view[0].
[0]http://www.openculture.com/2016/09/carl-sagan-the-dalai-lama...
https://www.theguardian.com/science/shortcuts/2014/may/14/po...
Nearly everyone is fine with this idea, but most everyone also thinks people with religious views different than their own will have trouble with it.
The major religions have already shown how they deal with evidence of outside of the garden of Eden. Several don't care, because the garden isn't part of their belief system to start with, and most of the rest have no problem with it (because they don't view the garden as literal), and the remainder just dismiss the evidence and distrust the entire field of science associated with it.
I don't think expanding that to off Earth is likely to change a thing about those responses, though the details of exactly which groups have each response might be a little different (though I suspect not much.)
I doubt it.
If the last few years have taught me anything, it's that no amount of evidence can dissuade someone from believing something they want to believe in.
Humans began in the Garden of Eden, but that's only one species, albeit an important one.
It is easier to square religion with life on other planets than it is to square the odds of evolution happening in a similar way on multiple planets.
I don't think it would change anything for them. We're living in a golden age of science, and that did not change anything for them. The existence of aliens would just be one more thing to either reject or literally bedevil.
Like they've dealt with every other scientific advancement that killed their beliefs. They will deny it as much and as long as they can until they will be forced to admit it, at which point "god" will shrink to an even meaningful pocket of scientific ignorance. Some of them will keep denying it forever
E.g. how would the major organised religions cope with the revelation (pun intended) that there was life that originated off of Earth/outside of the garden of eden?
For a lot of people who take religion seriously, I feel like this could be a major upset. It might not affect "day to day life" in terms of the lights staying on and there being food on the shelves, but there could be a significant personal impact on a lot of people which may lead to a lot of things like depression/substance-abuse/suicides/general-"fuck it, its the end end of world, I am going to <x>"-sentiment/etc that will have knock-on effects (e.g. not turning up for work, abandoning family/responsibilities, running away to live as a hermit in the woods, gun hoarding etc)