So, the Pope recently visited the UK, though thankfully not Durham, and there were numerous protests. As head of the Catholic church he's said a large number of extremely unpleasant things, and endorsed many anti-women and anti-LGBT views. Then there's the church hierarchy's treatment of numerous abuse cases across the decades. The protesting was hardly surprising.
One of the consequences of this, as well as the general justified sentiments against the Catholic church hierarchy and the Pope personally based on their roles in covering up abuse, recommending discrimination, and so on, has been various criticism of Catholicism and religion in general, and then from that general attacks on the idea of people believing in anything "supernatural" (including deities). There's a very short slippery slope from criticising the genuine problems with the Catholic hierarchy to anti-religious discrimination (protests are not a good place for fine distinctions like that, either, unless you're very careful).
The atheist criticism of religious belief is - in their1 own words - that it is "not reasonable", "not rational" or "not based on the evidence". The three phrasings are given much the same meaning in practice, and the disablist connotations of irrational (and the general insult of unreasonable) are generally desired.
I entirely agree that there is not sufficiently strong scientific evidence for the existence of anything that could reasonably be described as a deity, but that's really besides the point, and the use of "not reasonable" or especially "not rational" as shorthands for "not based upon scientific evidence" is extremely problematic.
I'm going to use "unreasonable" (note the quote marks) as a shorthand for "not based on scientific views of evidence and logical conclusions from that evidence" to save space, because even though that's not quite the normal meaning of the word, it's the meaning given to it in these debates. It's true that given that definition, belief in any deity or non-deific supernatural2 occurrence is "unreasonable". The problem is that so are rather a lot of other things that are commonly held beliefs and take place entirely within the natural realm.
Ethics and morals
Ethics and morals are unavoidably "unreasonable" (this is why straw-atheists don't have them). It is not possible to prove solely by the application of evidence and logic that a particular moral stance is superior to another stance.
Once you make some assumptions about what the purpose of having morals in the first place is - to keep society intact, or to maximise some measure of happiness, or to prevent certain behaviours, or whatever - you can then "reasonably" use evidence and logic to make a decision about the best ethical and moral decisions to achieve that purpose. But since your purpose was selected arbitrarily, and in practice based on socialisation and other factors external to your "reasonableness", it is itself "unreasonable".
Anything else that involves a values judgement - aesthetics, what to have for breakfast, etc. - ends up with the same situation.
The scientific method
The scientific method - in extremely concise outline - is that you make a theory to explain an aspect of nature, carry out experiments to test the theory, and refine or abandon the theory according to the results of the experiments. The idea is that over time the incorrect theories will be contradicted by experiment, and the correct ones won't, and the accuracy of the set of all current theories will therefore on average increase over time.
There's lots of added detail in practice to make sure that you don't throw out correct theories, or hang on to incorrect ones, in an attempt to get to the real right answer faster, but that's not really relevant here.
The scientific method is something I personally have a very strong belief in (the basic principle, anyway - I have quite a lot of criticism of some of the details of implementation, especially in some fields of study). It is, however, an "unreasonable" belief - I cannot prove, from the evidence, that the scientific method works.
I do have a straightforward circular argument in favour of the scientific method (summarised: "it seems to have worked so far"), but it's generally not considered "reasonable" - or indeed reasonable - to use circular arguments.
This might fall within the scope of "supernatural" for some people, but it need not. I believe that I have free will, and that so does everyone else. I don't even think it's philosophically interesting to discuss alternative situations where free will does not exist because I don't believe there's a self to exist without the existence of free will - there's just particles moving along their probabilistic paths.
I have no evidence of a scientific sort for this, and only a circular argument similar to Descartés "I think therefore I am" for non-scientific evidence. It's not a "reasonable" belief, but I think it's an entirely reasonable belief given the alternatives.
So, in praise of unreasonableness
The "sceptical atheist" community is right that religious beliefs and faiths are not "reasonable". Where they're wrong is the giant leap many of them take from that to "and therefore a sign of lack of intelligence / moral inferiority / mental illness / closed-mindedness / other insult of choice." and in the implication that one can get by entirely on "reasonable" beliefs.
This results in the usual problems that happen when one group of people believes another group to be inferior to it. These are all of course criticisms that can be applied to religions too, but atheists claim to be above the "irrational" actions of religion.
Firstly, while in the UK atheists don't have the structural power to discriminate against the default religion of Christianity (whatever the Pope might say), they are by a significant margin the second-most powerful belief group and so can quite happily contribute to the oppression of believers in religions lower down the local kyriarchy. See also France and the way an aggressive anti-religious message (masquerading as secularism) has been mixed with racism for a wholly counter-productive ban on Islamic veils.
Stereotyping the extremely diverse beliefs of a billion co-religionists to their most extreme members lends itself to being a cover for other forms of bigotry (most directly racism and disablism, and a claim that one is being "unreasonable" or "irrational" is an extremely common silencing tactic everywhere).
I don't want a situation where atheists end up at the top of the pile instead. This isn't going to happen any time this century even in a secularish country like the UK, but it shouldn't even be a goal - the goal should be to end religious privilege and discrimination, but that's a goal that many atheists would reject as treating "unreasonable" beliefs as valid.
Secondly, it makes it more difficult to get co-operation between atheists and religious people on mostly unrelated social justice matters. This also makes it harder to work together on matters related to the conduct of religious organisations where, to return to the start of this post for an example, the majority of both atheists and UK Catholics have serious disagreement's with the Catholic hierarchy's decisions on abortion, contraception, LGBT rights, women's rights, and so on.
You end up with the usual problem of intersecting oppressions, though perhaps with the default in the other place, where the existence and experience of Catholic LGBT people gets erased by both their own religious hierarchy and by their supposed allies, or action within religious communities in favour of women's equality is dismissed as irrelevant because it takes place within a religious setting.
There seems to be an attitude that because religious people have an "unreasonable" belief in one area, there's no point in trying to work with them in other areas despite this disagreement, but instead one must convince them of the truth of atheism first. This never ends well. It can also lead to an approach where people try to find scientific justifications for ethical decisions, and I've looked at one example of the problems with that approach before. Science is a valuable tool for humanity, but it's not supposed to be used for everything.
Thirdly, as I've said above, it misses the point. I don't believe in social justice because I have scientific standards of evidence that the world would be a better place without the kyriarchy - I don't even know what a non-kyriarchal world would look like in practice - but because I have what would be insultingly dismissed as "faith" that it would be better (according to my own ethical values) than what we currently have. I'm happy to hold that "unreasonable" belief and work towards it. Having decided "unreasonably" that this is a goal, my approach is going to be at times very much based on scientific evidence, of course, but that doesn't make the goal itself scientifically "reasonable".
Let's be "unreasonable", because there is too much that is important that cannot be dealt with "reasonably". Let's let other people have their own "unreasonable" beliefs, if they don't cause harm; and let's focus on the harm caused, not whether that harm has a scientific or an "unreasonable" backing3, if they do.
1 While my personal beliefs in deities and other supernatural things are very similar to those of a sceptical atheist, and while I agree that there is no scientific evidence for deities and the supernatural, I don't at all agree with the conclusions generally drawn from this, so I'm not using "our" here.
2 The definition of "supernatural" versus "natural" is hardly the dichotomy that it's made out to be - see Clarke's Third Law. Determining whether a "supernatural" event is really "outside nature" or just a sign that some previously reliable theories need refining would in practice keep people busy for centuries or longer. Meanwhile, by definition, anything genuinely supernatural would not be amenable to scientific study.
3 People asserting a scientific backing for their claims, when their claims do not meet general scientific standards, should be criticised for this, of course, and claims that are purported to be scientific can of course be meaningfully analysed by scientific methods.