The way the Talos Cult is handled in the vanilla game is, in my opinion, very different from the interpretation that TR's recent design documents have given it, to the point that I fear they no longer properly align. TR's Talos Cult is presented as an illegal, hostile and suppressed cult, a secret heretic organization within the Legion which is persecuted by the Empire. This does not stroke at all with the way the Talos Cult appears in-game, where it is implied to be a somewhat popular, albeit hermetic mystery religion with ties to both the Imperial Legion and the Imperial Cult, and only a minor splinter cell is actually involved in subversive activities.

To make my case, I've collected mentions of the Talos Cult from in-game dialogue:

• First mention in the quest journal: "Darius suspects that some of his troops involved with the Talos Cult are involved in some sort of conspiracy."
• Topic "Orders", General Darius: "Informants have told me of a conspiracy brewing involving the Talos Cult, but I have not yet been able to find any proof of this."
• Topic "Talos Cult", generic response: "I know they revere Tiber Septim, but there's nothing wrong with that. Not really of too much interest to me, though. They have many followers in the Legions."
• Topic "Talos Cult", faction member response:"We are those who worship the true following of the Legions. Protecting the Glory of Tiber Septim, Talos, the Dragonborn."
• Topic "Talos Cult", General Darius:
  • "They are a group that reveres Tiber Septim. It is not the group as a whole with whom I am concerned. It is rumors of a conspiracy within the membership that interests me."
  • "So you found a secret alter to Tiber Septim? It troubles me that the Talos Cult has been hiding its practices from me, but the worship of Tiber Septim is accepted throughout the Empire."
  • "You have ruined their treasonous plans, but now I wonder... If we cannot trust the Talos Cult, who can we trust?"

    
What I am getting from this is, that the Talos Cult as a whole is a respectable, popular, if somewhat exclusive group. Worship of Tiber Septim is (obviously) commonly accepted, and no one is surprised of suspicious if some Legion soldiers are members of the cult. Darius' suspicions only pertain to a small part of the cult, and then only because his informants brought this to his attention, not because the Talos Cult is in itself inherently suspicious. He is also not opposed to the fact that they have an altar room, only that they tried to hide it from him, which is suspicious precisely because Talos worship is so common and accepted. Most telling is his remark that, if the Talos Cult cannot be trusted, nobody can be trusted - implying that under normal conditions the cult is a faithful and reliable ally to the Imperial project.

In short, the Talos Cult is never mentioned as in any way heretical or questionable. In fact, several dialogue responses and books mentioned the Talos Cult in the same breath as the Imperial Cult, suggesting that they are closely allied or even somehow institutionally related - both being missionary cults in a foreign land.

• Topic "Morrowind Lore" savant response: "The Imperial cult brings divine inspiration and consolation to the Empire's remote provinces. The cult combines the worship of the Nine Divines -- the Aedra Akatosh, Dibella, Arkay, Zenithar, Mara, Stendarr, Kynareth, and Julianos -- and the Talos cult, dedicated to the divine god-hero Tiber Septim, founder and patron of the Empire."
• From the book "For my Gods and Emperor": "The cults combine the worship of the Nine Divines, the Aedra Akatosh, Dibella, Arkay, Zenithar, Mara, Stendarr, Kynareth, and Julianos, and the Talos cult, veneration of the divine god-hero Tiber Septim, founder and patron of the Empire."
• Topic "Talos", Imperial Cult response: "Tiber Septim was born on the continent of Atmora with the name 'Talos'. When he became Emperor of Tamriel, he took a Cyrodilic name -- Tiber Septim, the Dragon of the North."

    
Finally, it would make most sense for the Talos Cult to be a more-or-less mainstream organization whose views on the deity do not deviate sharply from the mainstream stuff espoused in The Many-Heade Talos and The Song of Tiber Septim: not only is this more in line with both background lore and later games, but it also makes far more sense that the generically named "Talos Cult" worships the orthodox Talos as opposed to the more bizarre deviant pseudo-heresies and doctrines espoused by the smaller Imperial cults. Some cultists outisde the Gnisis splinter faction could also espouse similar views (that the current Emperor is weak and does not honor the memory Tiber Septim), but the mainstream Talos Cultists would be loyalists, and not engaged in subversive ativities.

The specific role that the Talos Cult is to play in TR questlines and faction gameplay can, in my opinion, be maintained if it is either strongly edited or assigned to a wholly new cult, a splinter sect of talosite worship, oddball death cult similar to the syncretic brotherhood of Seth, or something like a Remanist cult (after all, the conquest of Morrowind would also play an important role in the worship of Reman, the Worldly God, which is something we have seen very little of so far in either the games or the province mods).