The third side of the coin
First off, I always appreciate queries that look into cultures, social structures and corporate motivations. Especially when the worldbuilder is trying to examine peoples and cultures that differ considerably from the human model.
You've gotten the psychological underpinnings and the SE specifics handled very well by Otkin and JBH.
I'd like to focus on the writing, basically a critique that I hope might give you some ideas for making your underlying query work better. (And yes! It's going to be long!)
In perusing the comments, I note that several of them can be interpreted in terms of writing. Particularly those that dwell on storybuilding vs worldbuilding, formatting, form without substance and the like.
If I were to have written a comment on the writing, I might have said something like it comes across generally as disorganised and disjointed; word choice and formatting leave me confused as to what's being asked. I not sure I wouldn't have closed for being story based or not! I can easily see why that was the overwhelming reason, though I think there are other issues.
First impression is almost always mechanics. Spelling, grammar, usage, formatting. SGUF. As a writer, I'd note that your spelling is not bad, but paying closer attention to the red underlines would reveal the few errors that exist. Worse are some odd word choices. Right off "a metaphorical children's book"? Do you actually mean "metaphorical", like the use of a commonplace item to mean something deeper? Or did you mean "hypothetical", like a book that you could actually write but are not actually writing because the purpose is other than writing an actual book. Or did you mean something else? Metaphorical may well be the right word! -- but you didn't really convince me. Thus, I see this as a red flag of the "how much of this long query am I going to have to parse just to ensure I get the OP's meaning right" kind.
The worst of the first impression falls under formatting. You begin with a basic description of what you're doing, which seems to morph into a description of the Chik'en character as a person and then into the Pil-Dalians as a group, to their perceptions and then to their observations.
Its unclear where the story starts, what the story actually is and what's descriptive and what's part of the story. I think this could easily be fixed with some (very tasteful) section headers. You might also consider separating the description of the Pil-Dalians from that of the Chik'en character. And speaking of the Chik'en character, you might want to replace the description of this specific character with a description of Chik'ens in general. That way you're looking at society vs society, rather than our society vs a visitor from eslewhere.
The writing itself is somewhat tedious. Word choices and sentence structures are odd. Grammar is not well construed. Style, I think, might be off putting to some (and I must disclose that it was off putting to me); yet I am setting that aside in the hopes of getting what I believe to be a good question clarified and reopened. I'm just going to look at one paragraph as an example of writing & stylistic issues:
One time, their Chik'en was seen trying to go out into Welford Lake so it could have a camp on the island. It would walk this way and that, putting things in the water, trying for a raft. A visitor came to the lake, which is a bit outside the village, with a boat on a cart, and he apparently wanted to do some fishing. The Chik'en stopped its raft-building experiments and hid behind a bush as the visitor arrived. The visitor went about untying his boat, and preparing his gear, and apparently went away to go look for bait. Perhaps some worms or grubs, as he was looking intently at the ground with a cup in his hand. The visitor disappeared into the shubs, but the Chik'en was seen pondering only a little, and then returned to Pil-Dale. It became almost a legend in quiet mutterings when the youthful kids who saw this returned. Certainly, if they had some desire to get to an island, and a boat was put in front of you, they would have taken the boat! Who would not? But carrying such a thing around would just be a bother, they only stayed to observe this curious creature. This created suspicions in the village, and people became wary of the Chik'en.
- "Their Chik'en": who are we talking about? Assuming this is the opening sentence of the story, I'd have expected to be clued in to who is doing what. Outside of the story, I know you mean the Pil-Dalians; but inside the story, we won't have the previous descriptive paragraphs. Which leads me to second guess not only my reading, but also your purpose: is this even a story, or is this just a continuation of the description of what the Pil-Dalians were planning?
- "Trying" doesn't make sense here. The Chik'en clearly went to the lake, so there is no issue of making an attempt. Since this is a report of what they saw, the first thing they would have seen is the Chik'en going to the lake.
- "It, he, they, etc." Pick a pronoun and stick with it! Since you're dealing with a specific character, pick she or he and remain consistent.
- "Have a camp" doesn't make sense. "A camp" of course can mean many things such as a public grounds for camping, a military base, a small cabin or house situated in a recreational area that one does not live in permanently. I suspect the Chik'en wanted to "go camping".
- "Would" is not the right verb here. "Would" can express a bajillion things in English, but it seems that a simple past tense would be the best choice here. As it stands, I think the clearest reading of this sentence is one of habitual action, which is, I think, not what you're going for.
- Comma splice. This sentence and the next one read almost as comma splices. The concatenation of motifs separated by commas is probably not the best style choice overall. But I could be convinced otherwise if your plan is to write a "dialect" story.
- "Try for" is of course a phrasal verb, most often with a goal or something intangible as its object. Here, I'd have expected the simple verb "try", "trying to make a raft".
- "Apparently". Too many in close proximity. Either pick a synonym or don't ascribe motive to the characters, especially since you've specified that this is "what they found out" about the Chik'en's behaviour. Why would they be interested in determining the motivation of a fellow Pil-Dalian? Repetition can be useful, but I don't think it adds anything here.
- "Pondering". Again, ascribing a motivation or assuming an interior state of mind. He could have just been daydreaming about grubs!
- "only a little". Only a little what? As written, "a little" describes the quality of the pondering: in other words, he didn't think much! I got the feeling that they were trying to describe a relatively short space of time; and if that's the case, I'd have expected "he was seen pondering only a little while before returning...".
- "It became almost a legend in quiet mutterings when the youthful kids who saw this returned." I'm not certain how to read or connect "in quiet mutterings" with the rest of the sentence. Generally, we don't "mutter" legendary events. We might whisper them furtively or tell them excitedly. "...when the youthful kids who saw this returned." "Youthful kids" is a tautology. "Returned" is a little unclear in the context of a relative clause. Who is the subject of see and returned is the object of see. What this means is that the children "saw some thing or object returned to someone". I don't think that's what you meant; I'd have expected "...who saw the Chik'en's behaviour returned home."
- "... if they ... in front of you ... they would" Don't vacillate! Again, keep pronouns consistent. Pick one and stick with it.
- "But carrying such a thing around would just be a bother, they only stayed to observe this curious creature." This one is a comma splice. Also a non sequitur as the second phrase does not follow from the first and the first doesn't logically lead to the second. Carrying the boat is clearly connected to the previous idea of stealing a boat, but observing the creature ought to be excised. It doesn't fit anywhere. You could edit this phrase to introduce who did the observing and something of the manner of the observation and put it up in the beginning of the paragraph. This would solve the "Their" problem!
- "An island". While not incorrect, it doesn't seem the best choice either. Since "the island" out on Welford Lake is already an established place in this paragraph and in the awareness of the kids doing the observing, I'd have expected them, or the narrator, to refer to it as "the island" in the context of considering the stealing of a boat. Thematically, it would tie the strange actions of the Chik'en to the local geography of the Pil-Dalians.
- "This created suspicions..." What created suspicions exactly? What's the reference? I'm pretty sure your antecedent is "everyone in Pil-Dale was a taker by nature" from a few paragraphs ago, but the Chik'en has done so many things just in this paragraph that the antecedent ought to be specified.
Over all, the style seems to read as a kind of stream of conscious dialect tale. Some random things happen and things are described in a way that's more reminiscent of a grocery list than a story. It comes across as rambling and overly intimate. It lacks narrative cohesion. This can be perfectly fine when done well and in the right context. I think you could have done the stream of conscious better; but I don't think a SE question is the place to show it off like this!
Part of the disjoint I mentioned earlier I'd argue stems from the insertion of the story itself. It seems like the Pil-Dalians are trying to understand what makes the Chik'ens tick, but you are inserting a story about particular individuals and their own motivations and biases and misunderstandings which I think ultimately breaks the question.
What can be done? Given that your Meta question is "How can I portray a cultural response to a stimulus that avoids looking like a specific character’s motive?"; I think the best thing you can do, honestly, is to delete the story that happens in the middle of the Main question. Honestly, if it were well written and entertaining and seemed to mesh with the underlying question, I'd probably give it a pass. But slogging through something that looks like a very rough first draft and is not terribly entertaining and doesn't really mesh with the question at hand I think its inclusion is more detrimental than helpful.
A couple of the comments focused on the fact that your story relates to a single character rather than a whole society. This makes it almost impossible for me to overlook the individual Chik'en's actions and motivations. I understand why you'd like to use a single character to represent a whole culture; and I also think that doing so would actually work in the context of a story that is part of a book of stories about the weirdness of the other and coming to grips with it. It does not work in the context of a WB.SE question.
These problems can be fixed by the usual process of editing & rewriting. Basically, reread and rewrite the story itself for SGUF and for narrative interest. Reread, edit and possibly rewrite and reformat the question itself. Above all, if you're going to use a story as background for a question, please make me want to read the story rather than have to slog through only to end up not getting the connexion.
On second thought, if you really do want to keep the story as background, I'd suggest shifting it either to the very end, where it can be used as a reference, or else putting it at the top with a note that this is a story that you've written and that respondents are to understand the story, not as a narrative, but as a cultural object that you have a question about. It still needs editing and rewriting, but at least this way the story's presence is given a context.
Lastly: Get Your Story Straight! In your Main query, you specifically ask for an individual's motives:
But why? Why did the Chik'en cross the very dangerous Road?
Answers are based on motives that are consistent with the plotline and the unique social norms of Chik'ens.
Here in Meta, you declare that you want to ask about cultural or social phenomena, not individual motives:
How can I portray a cultural response to a stimulus that avoids looking like a specific character’s motive?
The story you told is all about an individual Chik'en. Even though he is a representative member of all Chik'endom, he is also his own person and has his own quirks, his own story, and worst of all, he has lived in Pil-Dalia for some time and is thus culturally contaminated. What you're portraying in the story has to be some unknown admixture of his native Chik'en culture, his adopted Pil-Dalian culture and his own particular personality as it is informed by these two cultures.
Careful attention to composing the query and writing the components of both the query and the story will go a long way to making your question reopenable.