A Friendly Empire.
A major external grouping with economic & miltary power that claims to be on the Bonehead side (at least for appearances sake, because they have to etc) but is actually rather weary of propping up this anachronistic shower at huge public expense. Often the Empire was party to the origination of the feud.
Boneheads will wake sweating in the night, certain that they are about to be betrayed, sold out, stitched up by the Empire who claim to be their friends but are treacherously trying to get the Boneheads to "talk" to the Others.
Boneheads must share a common bond, something that sets them apart from and preferably slightly above the rest of humanity. Religion generally fills this role perfectly - major tradition or minor sect, it doesn't matter as long as it offers a pervading world view of the pagans (both Friends & Others) beyond the walls. Culture normally extends it: odd kinds of food, specific musical instruments or dances - a repetiore of tuneful songs with ugly lyrics is usually in there somewhere.
An obsession with History.
The Bonehead position or possession is invariably founded on hundreds or thousands of years of glorious Bonehead History, generations of their ancestors who fought & died, whose Bonehead blood stains the whatever it is that the Boneheads want to keep (usually land). Or at least that's what the History that they teach Bonehead children proves - and they'll publicly tar & feather anyone who mentions airbrushes.
Lessons from Bonehead History relevant to present circumstances must (not matter how glaringly obvious) go completely unnoticed (and be dismissed in sheer disbelief if pointed out by those who can't be expected to understand as they aren't fifthteenth generation Bonehead). Anyone elses' history is irrelevant (except the Others history, which is a pack of lies).
Above all, Bonehead events of several hundred years ago are always more important than the present or (obviously) any remaining future. This History must be celebrated regularly & publicly, so the Others hear & understand that a point is being made. (E.g. schools must close & a public event be held to mark with march & song the Historic annual Anniversiary-of-when-we-killed-hundreds-of-Others-long-ago Day).
Complete & utter un-viability - economic, military or both.
Boneheads must understand that their whole way of life is fundamentally dependent on outside support - that without the enormous generosity of the Empire that claim to be their friends (usually in bankfuls of cash, waiting squadrons of aircraft carriers &/or boatloads of troops) the Boneheads & the whole Bonehead way of life could be wiped out in a week. But a true Bonehead must never mention or admit that to anyone - least of all themselves. Admitting that would mean admitting that the only way the Boneheads could survive (let alone prosper) in the long term would be by talking to & compromising with the hated Others.
A common origin
It is usual to find upon investigation that the Boneheads and the Others were once the same, that they once shared the same language, land & culture before being separated by Empire or religion. This will be denied vermently by all parties.
So there's my template for Boneheads. You can join in: look around at your newspapers & your TV news - see if you recognise anyone shouting "NO!" very loudly.