To add to the others, Hinduism, Jainism, Buddhism - they all take it for granted that there are multiple world systems in traditional accounts.
As for Christianity - the Bible already says the world is only a few thousand years old by implication. Many Christians who are scientists have no problem with that, because they don't go to the Bible as a source book for science. Science doesn't seem to be its strong point. Its account of the creation can be thought of as an insightful mythology, or to be read in other ways.
Science in its present form didn't really exist back then. So I expect it would be the same, anyway it is just an "error of omission" - I suppose if you believe in an omniscient God (which I didn't really, not in that sense, as a Christian) - you might wonder why he didn't tell us about those other worlds. But why would he.
As an example of Christian literature exploring other worlds with life on them I like C. S. Lewis's stories. Not the stories of Narnia though they do after a fashion suggest a magical other world. But you can check out his "Out of the Silent Planet" which imagines life on Mars with intelligent creatures there. He imagines them as somewhat "unfallen" creatures in the Christian sense leading to entertaining writing.
It was my favourite in his science fiction trilogy.
Could be like that, or could be that they have their own Christ figures. But given that the world has many countries that have other religions, which don't resemble Christianity at all, why assume that Extraterrestrial religions resemble it either? Surely they would have as much diversity in this as we do, possibly more so, religious ideas or philosophies that no human has thought of (or however it is they get started, inspiration or whatever).
So then why should they be of more problem to any religions than the hypothesis of existence of other continents and islands, later confirmed?