I'm tired of such preoccupation on some nebulous notion of "rationality," when any cursory reading of philosophy, particularly of mathematics, informs one of the subjectivity inherent in the choice of one's axioms and definitions, especially amidst type theory's recent resurgence.

So, no: "rationality" is not common knowledge. Perhaps I don't accept the Axiom of Choice, yet you do? Perhaps my definition of "authority" differs from yours?

I am reminded of Richard Hofstadter, who said something to the effect of: "anti-intellectualism is the idea that my ignorance is just as good as your expertise."

Please don’t confuse rationality with rationalism.

Nor we should reduce it to inferential processing of axioms and propositions. I’m surprised your cursory reading of philosophy haven’t encountered for example the Aristotelian golden ratio (root word for reason) and its application in virtue ethics, or the word logos that the entire christian culture was built on, or that should be familiar to anyone that has studied anything -logy.

We all actively participate in rationality with varying degrees of success. And calling out personal attacks made at the expense of actual counter-arguments is rational both in the sense of proportionality, appropriateness and even as a call for virtuousness.

I'm sure you are using it in the pursuit of rationality, but I think it's holding you back. It's good to know common fallacies because it helps you understand the trappings that you and others may fall into, but it's not a silver bullet, mainly because some logical fallacies are a direct result of shortcuts that we must make for human society to operate at its current scale. Common thought biases (such as confirmation bias) also directly result from this. Take for example the following:

1. Appeal to Authority

An appeal to authority can be a good sign that someone does not actually know what they are talking about and are regurgitating the words of some pundit. However, the progression of human knowledge at the rate we enjoy it today entirely depends on specialists of their particular field deferring to the knowledge of an authority outside of their field. And laypeople have basically no criteria to use to select which authority will tell them what they “know” except for perceived credibility of the authority (see “Ad Hominem”). A simple example is the roundness of the earth. Can most people derive from first principles an empirical method that would allow them to witness first hand the curvature of the earth? No. Most people must take the word of scientists and mathematicians this for this at face value (at least, they did until airplanes and photography were invented). In the scheme of things, though, it's relatively simple to demonstrate that the earth is round; other things are not so simple. The sum total of human knowledge is built upon a hierarchy expertise and authority where each higher layer depends on the correctness (or correct-enough-ness) of the layers below, the vast, vast majority of which individuals at the top layers cannot verify even a little bit, let alone 100% (Hierarchy might not be the correct model here but it's a simple short hand). When two non-experts in a field are arguing about something, practically speaking, they are either depending on the knowledge of a multitude of authorities or they are talking out of their asses. 99.9% of discussions regarding any given topic online could probably be said to fall into one of those two categories.

2. Ad Hominem

As being able to trust in the authority of experts is such an important aspect of confidence in your conferred knowledge of something, you must consider the reputation of that authority when choosing what to believe. As such, if you do not have the expertise to personally establish on a factual basis that what someone is saying is wrong, you can only consider the credibility you perceive them to have (or become an expert yourself, which is simply not a scalable approach). If someone is telling you that a salesman has a reputation of selling faulty products, it is not fallacious reasoning to use their lack of credibility to inform your decision not to buy whatever they are selling, despite your inability to personally examine the quality of the product for sale. Or, I should say, it is considered fallacious but is actually not flawed reasoning by any useful metric.

The above “fallacies” are rooted in, essentially, tools that we must use to make decisions at a reasonable pace. Pointing out that someone has used one of these tools isn’t particularly productive when they are a necessity. I’m sure there are more like this, but none come to mind at the moment. There are more “fallacies” still that are just plain abused, for example, the Slippery Slope. People misunderstand this one, unfortunately. They see a slippery slope argument and think “Aha! That’s a fallacy! You are wrong!” I’d call this the fallacy fallacy but that would be saying that their only mistake is to ignore the substance of the discounted argument. The problem is, there actually ARE slippery slopes! It’s an exercise in taking a process to its natural conclusion given that several steps naturally follow. The fallacy only occurs when the slope isn’t actually that slippery or the steps don’t naturally follow.

There are, of course, fallacies that practically always result in flawed reasoning, such as Circular Reasoning. Some of these I think it’s safe to just call them out as totally garbage.

In summary, some arguments are mis-identified as fallacious, often the Appeal to Authority, Ad Hominem (and to a lesser extent the Slippery Slope, among others), because their inclusion on the list of fallacies makes people think reasoning that relies on them can never be sound. This belief could not be further from the truth.

I'm agreeing with you, but I want to say a bit more about appeal to authority.

Appeal to authority is exactly as valid as the authority. The way "appeal to authority" is a fallacy is usually something like "Y says X", where Y is not actually an expert on X. Y may be a politician or a pundit, or even a scientist outside their area of expertise. (Scientists should be less eager to opine on subjects outside their expertise, but hey, we're here on HN, and we do it all the time, so...)

The other way it happens is "Y says X", and Y is an expert on X, but Y has a fringe view on X (or we could be charitable and call it a highly minority view on X). This is harder, because you can't detect that just by examining Y's credentials.

But if you disallow all appeals to authority, then you're left with just each person's own arguments and knowledge. And why do we think that's better? Why do we think that the personal opinion of amateurs is more valid than the considered opinion of experts? So we have to allow appeals to authority (as you said).

The trick is to only flag the fallacious ones. I say "the trick", because it is not easy...