Don't atheists have faith in science just like religious people have faith in God?

In a sense, that is correct, but only in a very simplistic sense. Religious people who make this argument would do well to heed their own counter-arguments when we atheists say that faith is not a virtue. One of the ways religious people respond to that criticism is to say that "faith" doesn't necessarily mean "blind faith;" it can also mean "justified faith" (as in, "I have faith that Steve is a loyal friend because he's proven his loyalty over and over again"). Blind faith is believing something without any meaningful evidence, whereas justified faith is being convinced of something because of evidence, but recognizing that due to the problem of induction, you can never be 100% sure that there isn't some further compelling evidence in the other direction that you just aren't aware of. I think we can have justified faith in the scientific method and the scientific community.

In my case, I did a lot of personally examining the evidence in favor of evolution; I was actually so indoctrinated by creationism that I continued to believe evolution was dumb even after I stopped being a Christian. But then eventually I decided that I should look into the evolutionist rebuttals to creationist claims, and I found the rebuttals to be far more convincing, and backed up by far more evidence. And whereas creationists claimed that evolutionists were just dishonestly propagating a science they knew was false to validate a specific worldview, the creationists were the ones who openly acknowledged that they would simply ignore or discard any evidence which goes against the conclusions they already had going in.

Bottom line, my examination of the evolution issue was pretty thorough and in-depth, and I don't really think I believe in evolution based on faith (even justified faith) in the scientific community. Yes, there are always things that we don't experience firsthand, but there has to be a limit of reasonable skepticism to what information we doubt just because we didn't experience it firsthand (analogy: somebody doubts that a certain law was passed, and you show them the text of the law straight from congress.gov, but that doesn't convince them because hackers could've just planted false information on the official government website; yes, it is technically possible, but it's outside the realm of reasonable likelihood). If a person is going to be that skeptical and that demanding of firsthand experiential information, then I would fully expect that they're only applying that extreme level of skepticism to worldviews they disagree with, because there's no way their own beliefs would hold up to the same demand (unless, perhaps, their own worldview is full-blown solipsism).

Anyway, bit of a tangent. The point is that I have investigated evolution myself quite thoroughly, and found the position of mainstream science to have far more hard evidence to support it. So then, when people attack the position of mainstream science on issues like climate change or vaccinations, I see a lot of similarities between their lines of attack on those issues and creationism. I haven't done a tenth of the research about climate change that I've done about evolution, so yes, I do have some degree of "faith" in the scientific community on that issue, but it's faith that is justified by my more in-depth examination of how science gets the job done on the issue of evolution (and some other minor issues that were quicker and easier to research).

So that's the main way that I would respond to this criticism, but there is one other small point worth mentioning. I think another way our "faith" in science is different from the religious faith that many believers have is that it's subject to change in light of new information. There are many religious people who actually take pride in the fact that their beliefs wouldn't change no matter what new information came to light (like William Lane Craig saying that the ultimate evidence which supersedes everything else is "the self-authenticating witness of the Holy Spirit," i.e. a gut feeling). But the thing about having some degree of trust in the scientific community is that you recognize it's just humans doing the best they can, not some divine word from on high, so I think that makes it much easier to be humble and accept that we should be open to new information potentially changing our position, instead of blindly walking in lock-step with whatever mainstream scientists believe at the time. But I do think that once you've done enough research for yourself to see that mainstream science isn't just some shadowy cabal of people trying to foist a specific conclusion on the unsuspecting public to support some selfish worldview, then it does make sense to take an "innocent until proven guilty" approach to the mainstream scientific consensus on an issue. Because, as others have said, it works; it gets results.

Do you think religious people would change their beliefs if the existence of alien life were proven?

I couldn't disagree with that idea more strongly. You have to understand the psychology of belief, that when religion is a deeply-integrated part of a person's identity, they don't change their beliefs when provided with new information; they filter that information through the beliefs they already have and refuse to give up.

I'll give you two anecdotes which I think illustrate how some religious people would react to this (and that's not even considering the people whose religious beliefs are legitimately compatible with the existence of aliens). The first is personal, the second is a public figure. The personal one is myself; I used to be very religious. I remember one time back in those days, I started to watch the movie Paul (by that time, I was cool with R-rated movies despite being very morally conservative). There's a point in the movie where the two guys and the alien run into a fundie Christian, and the alien says his existence "disproves the notion of the Abrahamic, Judeo-Christian God." I actually turned the movie off right then and there, not because it was blasphemous, but because I disagreed so passionately with the assertion that the existence of aliens would disprove my beliefs. Mind you, I didn't have any well-thought-out theological ideas about how the existence of aliens would coexist with the truth claims of Christianity, I basically just thought, "Christianity is obviously true, whether aliens exist or not. The end."

Now, the public figure; Ken Ham. This blog post from AIG gained some mainstream attention when Huffington Post reported on it with the headline "Creationist Ken Ham Says Aliens Will Go To Hell So Let’s Stop Looking For Them." In fact, the main thrust of the post is that aliens obviously don't exist, because the Bible says that people and animals were created by God, not evolved, so there's no reason to think there would be any living organisms on any other planets. He even ludicrously claims that the whole reason scientists are trying so hard to find alien life is to disprove creation so they'll have free rein to rebel against God. That seems to go right along with your theory that if the existence of aliens was proven, religious people would abandon their beliefs, right? But look closer; there is a point in the post where Ham says, "Now the Bible doesn’t say whether there is or is not animal or plant life in outer space," and later, "this means that any aliens would also be affected by Adam’s sin, but because they are not Adam’s descendants, they can’t have salvation." So, within this whole rant about how we should stop looking for alien life because aliens obviously don't exist from a Biblical standpoint, he's still not going so far as to claim that the existence of aliens and the truth of the Bible are utterly incompatible. He's essentially making a falsifiable claim, but with the back-door exit already wide open if that claim is ever actually falsified.

If "we" find out that aliens exist, then the first step for fundamentalist religious people will be to simply deny the truthfulness of that claim (just as they already do with evolution, because they believe it contradicts their beliefs as well). When the evidence becomes too strong to deny (like, if aliens live among us), then they'll shift to claiming that their beliefs were always consistent with the existence of aliens, and will even find verses of scripture that they can twist to claim that the Bible (or whatever other scripture they believe in) already told us that aliens exist, so it must be inspired by God because no human could've known that way back then.

Flat-earth theory is a good real-world analogue to show both stages of the process. There are people who still vehemently oppose the idea of a spherical earth, because they believe that the Bible indicates the earth is flat. Conversely, there are people who point to verses like Isaiah 40:22 as the Bible presciently acknowledging that the earth is a sphere, even though the vast majority of translations interpret the word as "circle," which is a flat, two-dimensional shape.

The most ludicrous example I've ever heard of this (a person trying to twist the words of the Bible to make it seem like it indicates foreknowledge of modern scientific discoveries) was from Hugh Ross. He said that the Bible talks about the universe being constantly expanding; my ears perked up when I heard this, because I've read the Bible a few times, and certainly didn't recall seeing that. So then, he read the verse that he claimed supported that contention. It was actually the latter part of that same verse, Isaiah 40:22, which says God "stretches out the heavens like a curtain and spreads them out like a tent to dwell in." I'm sorry, do curtains or tents continuously and endlessly expand throughout all time? Of course not, they expand to a certain size and then stop. This verse is obviously not saying anything about the universe constantly expanding. All Ross did was take what we've learned through real scientific discovery and combine it with his dogmatic belief that the Bible is the inspired Word of God, and then interpreted what it says through that framework. There's nothing about the proven existence of aliens that would make it impossible for people like him to continue using that approach.

How can you trust the scientific method when it can't be verified by the scientific method?

In the Q&A portion of this debate, an audience member asks Christian apologist Dinesh D’Souza, “on what basis can you dismiss the principle of parsimony?” D’Souza replies by glibly showing that you can't use the principle of parsimony to show that the principle of parsimony is valid. This is very similar to the oft-used argument (especially by William Lane Craig) that you can't use the scientific method to show that the scientific method is valid. The problem with this type of argument is that things like parsimony, science and the rules of rationality are methods for validating propositions. You can't use the scientific method to prove the scientific method, because the scientific method is not a proposition. It's not either true or false; it's an approach, a style, a means, of finding out which propositions are true or false.

You can't prove that a recipe is true or false (in the sense of being the one right and true way to bake a cake, for instance), but that doesn't mean you shouldn't use the recipe. What matters with a recipe is not whether it can be shown to be propositionally true, but what it results in. If you use a recipe for a cake, and the result is a really good cake, then keep using the recipe. It doesn't matter that you can't show it to be propositionally true, because it gets results. So it is with things like the scientific method and the rules of rationality. They're not validated because we can show them to be true (remember, a method can't be either true or false), they're validated by the fact that they get results.