>To people who use those things avoided, it comes off as arrogant.
[...]
, the listener who uses mutable state views the FP's attitude as judgemental

I disagree with your meta-analysis of where the root of perceiving "arrogance" comes from.

(I'll shall attempt to speak for non-practicing functional programmers and the following opinion is not my own.)

In my observations, it's that all the essays and evangelizations about functional programming do not manifest themselves in the industry as irrefutable evidence that it creates better programs, with less bugs, at higher rates of productivity.

For example, folks can point to Jane Street using OCaml, or a London finance shop using F#, but are they doing 10x better than Goldman Sachs using the clunky C++ language? Maybe. But we won't know because there are too many confounding factors.

Functional programmers can repeat all the "benefits" of the style with "immutable", and "referential transparency", "monads", etc, and describe languages in glowing terms such as "Haskell has this beautiful internal mathematical consistency that Java doesn't" or "Lisp with its homoiconicity lets you write a DSL as first-class concepts with macros whereas C++ makes you force-fit them into classes", etc, etc.

All those bullet points may be true but it doesn't manifest itself as obvious slam dunk winnings in the industry.

That's the root of the arrogance: the attitude of "superiority" about functional ideas does not match what people see on the street. In other words, people wonder why there are no AAA game studios using functional programming that blows everyone else out of the water crawling on their hands & knees with C++. Or some application software company using Haskell to deliver software with 10x less bugs, 10x faster, and 1/10th less cost than their competitors using Java. Or some YC company using 100% functional language and killing their competitors stupidly using Python/PHP.

So far, there are hundreds (thousands?) of tutorials about monads and recursive Fibonacci snippets but very few case studies (if any) of real companies killing the competition as a direct result of the functional programming language. Companies showing massive industry results is how you win hearts & minds. Fibonacci exercises are not enough.

What the functional community needs are better essays that go beyond "monads" and addresses why the mystery gap exists between functional theory and industry results. My guess is that the functional benefits are real but there are other aspects of software craft that overwhelm its advantages. In other words, the essays needs to look at functional style holistically.

As a historical analogy, the benefits of structured programming languages vs machine language were initially debated in 1960s. However, within less than a decade, everyone adopted it because the multiplication of productivity was obvious and compelling. The ease of programming wasn't just a 10x improvement, it was arguably a 100x improvement. Now, assembly is only done for isolated pockets of tight loops and resource constrained scenarios.

If the FP>OOP is similar to Structured>Assembly, then for some reason, the real world has not shown that same magnitude of increased benefits. Fix that perception and the root of "arrogance" goes away. Today, we don't say one is "arrogant" for explaining that structured programming will allow teams to write software faster with less bugs.

Imo, that's the type of self-reflection that functional essays are missing.