Before I begin, a quick disclaimer: I am not very lore knowledgable, and I do not know what other visions for the area exist other than a "little Orsinium" enclave with little conflict beyond border skirmishes.
The dunmer (especially the Temple) are ashamed that there's an enclave in their province that they do not control. Because they are ashamed, they will not acknowledge that it is outside of their control, and thus cannot openly conquer it. The orcs worship Malacath, who is a corner in the House of Troubles. The dunmer use this Malacath worship as a pretense for their aggression, and they present it to the rest of Morrowind as though it's just a crazy cult in the mountains in comfortably dunmeri lands. The truth of this "Shadow War of Marakh Bazhul" is suppressed as much as possible.
This brainstorming started with the idea of having a non-ruined daedric shrine in Marakh Bazhul. The architecture would be the same as the regular daedric shrines, except that there are no broken pieces, and the textures are fresher and cleaner looking (I'm thinking brighter, redder, and the white lines are more distinct). This would of course be a shrine to Malacath, since Marakh Bazhul belongs to the orcs, and this would of course be despised by the Temple, since the Malacath belongs to the House of Troubles.
So why hasn't the temple just sent in Ordinators to raze the shrine? They have. They do so repeatedly. But, every time, Malacath demands that the shrine be rebuilt every time as a pristine monument of his defiance against the Tribunal. When the ordinators invade, orcs from all across Marakh Bazhul rally to try to hold the shrine. Sometimes they succeed, but even when they do, they lose 3 to 4 orcs for every ordinator. For each orc, Orckish honor demands that he gives his life to the cause, and the better trained, better equipped ordinators are all to happy to take it. In Marakh Bazhul, a death in the defense of the shrine (which needs a name) is a prestigious honor.
So why, then, hasn't the government of Morrowind simply cleared out this unwelcome enclave? Because in doing so, they would have to publically admit the existence of Marakh Bazhul, and this would be a sore wound to their dunmeri pride, so the Temple performs these brutal shrine raids largely because it provides a "legitimate" pretense to attack/subjugate the orcs. This secrecy of Marakh Bazhul also retroactively explains why nobody ever talks about Marakh Bazhul despite it being such a notable place -- The Temple does what it can to censor its existence, or to misrepresent it as being a majority dunmer area with a few orckish "bad actors" at this one shrine. In addition, the Nords might have guaranteed its independence, as the nuisance in Marakh Bazhul takes resources away from the conflicts in Uld Vreach. I could also see the not-technically-war in Marakh Bazhul as a proxy-war in the informal struggle between the dunmer and the nords
The Redoran, who have no choice but to be aware of Marakh Bazhul, are not allowed to invade it for the reasons previously elaborated, but they are even more disgraced by its existence than the Temple, and they resent the Temple for stifling their initiatives to conquer it. This resentment is mostly prevalent in the military parts of Redoran society; the average Redoran commoner knows little about this conflict unless they happen to live right on the border. I also think the border is more peaceful than it has so far been considered, since most of the orckish fighting is happening within Marakh Bazhul's borders. Incidentally, I think this undeclared Temple war is broader than this one shrine to Malacath, but the shrine has a special place in the Bazhuli heart as a symbol of their perseverance. Characters who acknowledge this undeclared war might call it the "Shadow War of Marakh Bazhul". That might also serve as a good book name about the conflict.
Inside of Marakh Bazhul, I imagine it being mostly orcs with a notable minority of Nords, and dunmer largely relegated to outposts and maybe even ancient dunmer strongholds. I think Bazhuli orcs should have a heavy disposition modifier against dunmer.
With regards to the timeline of the orckish enclave, I see it as starting all the way back in the first era, and I see its continued existence as a point of pride among the orcs who live there. I do not know TES history very well, but I suspect it has changed hands between the nords and the dunmer many times, and only been independent rarely. For extra flavor, perhaps it was independent for while (a century or so?), and this was a "Bazhuli Golden Age" back to which Bazhuli orcs often heark.
As for why the average dunmer wouldn't know about Marakh Bazhul despite it being so old, they would have heard the Temple's narrative that it was conquered fully by the dunmer, and that the conflict was therefore over. The orcs and their sympathizers frantically trying to get the word out, but they're in an information war with the Temple, and they're losing. When a bookseller stocks this book outside of Marakh Bazhul, they stand a considerable chance of "mysteriously disappearing". While it's possible that the Temple publishes information to "debunk" the Bazhuli orcs' claims, I think outright suppression is the more likely approach to be taken.
With regards to the internal conflict among orcs about whether Trinimac still exists, I've pictured Marakh Bazhul as being largely Malacath loyalists. It seems like a divided Marakh Bazhul would not survive the ages.