Starting with Oblivion, the Elder Scrolls games have deemphasized politics and religion in favour of epic struggles. Their focus is on individual characters, either paupers or princes. Tamriel Rebuilt, in contrast, focuses on the middle managers and the macropolitics.

A lot of lore was developed (both in-game and out-of-game) to explain the differences between the First Pocket Guide and the settings in Oblivion and Skyrim. Most well known is "From The Many-Headed Talos", a text that Michael Kirkbride posted on the now-offline Bethesda lore forums, shortly after the release of Oblivion, which tried to reconcile the description of Cyrodiil in the First Pocket Guide and Morrowind’s dialogue with the pastoral landscapes of Oblivion. Skyrim directly quotes half of it through Heimskr’s sermons in Whiterun, leaving little question that the whole work is officially recognized.

This lore does not apply to Tamriel Rebuilt/Project Tamriel. We built our mods on the older lore and our Tamriel looks wildly different.

The Thousand-and-Eight Nibenese cults still exist, as do the Nords’ totemic tradition and their Old Gods. Cyrodiil is still largely a jungle where the tigers roam, and Skyrim an icy wasteland dotted with Direnni ruins in the Reach and Dwemer ruins limited to the Velothi Mountains in the east. The Falmer were by modern knowledge nomadic and left few traces of their existence behind.

The Thu'um is not a nearly forgotten legend, but a craft taught in the Imperial College of the Voice and part of family traditions, with the Greybeards' monkish teachings merely being the most well known to outsiders. By the ignorant, it is sometimes misidentified as another take on magic, but it is very much understandable to your average citizen.
Necromancy is legal and accepted (to varying degrees) in the Empire, and communication at the highest level of the Curia is conducted via Dreamsleeve memospores, as it has been since Reman's time. 

There is not one kind of dragon that has gone extinct (or not), but several: Akaviri war mounts are the symbol of the Empire and their descendants live on Tamriel among western dragons, while Cyrodiilic river dragons bathe in the Niben.
The Order of the Blades is just a fancy name for the Imperial Secret Service and while some of its members serve openly as protectors of the Emperor, most of them are tasked with intelligence work and are not readily found.

Politics diverge as well. The Nordic kingdom of Haafingar, exploiting prolonged Imperial weakness, has only recently occupied the Imperial territory of Roscrea and is now stretching its greedy fingers towards Solstheim. The Oblivion Crisis, hinted at in Morrowind's dialogue, is the result of prolonged unrest in the Imperial Province, as people fear the heirs of Uriel Septim VII are just Daedric doppelgangers planted to create disorder and ruin.

Prequels in an ongoing franchise are always problematic and Elder Scrolls Online is no exception. Its plot has been progressing and keeps shining light on areas which have been implemented differently in our projects, and retroactively invents politics that make no sense in our Tamriel or even the Tamriel of the mainline games. Time will tell to what extent the mainline continuity will incorporate the lore of ESO (and Legends, for that matter).

In any case, its position in the (not-quite ancient) past makes ESO’s plot and lore developments unpredictable for a mod set in the late Third Era. Even outside of Tamriel Rebuilt/Project Tamriel, ESO has in the past sometimes been assumed to take place within a Dragon Break to reconcile the larger setting. As far as our continuity is concerned, this might as well be true. The future of ESO’s Tamriel is not and cannot be the past of ours.

Responsible for creating the “modern” metaphysics of The Elder Scrolls, MK was busy creating lore to reconcile the difference between Morrowind and Oblivion out of a labour of love for the series and setting. From this spiralled ever more complex and hidden plots, metaphysics, and divine politics, attracting people by the mental exercise and colourful imagination.

As far as Tamriel Rebuilt/Project Tamriel are concerned, MK was one developer of many and the gnostic and secret lore he created is but one aspect on which we base our continuity. As a game mod depicting people living in a fictional setting, we are first and foremost concerned with Tamriel’s mundane reality.

At a fundamental level, history in The Elder Scrolls is different. Magic is a fact of life and just another craft. History is indistinguishable from religion. Souls are born, die, and are born again, and wizards who have lived long enough know this for a fact.

Most people Tamriel Rebuilt/Project Tamriel depict could never conceive of the esoteric truth Cosmic TES is concerned with, and so we must keep it confined and remember that it is secret knowledge for a reason. While daily life in Tamriel might be more magical than our reality, the world and its conventions are normal to its inhabitants and this is the reality we want to display.

Cults have their places on the fringes of polite society, and Imperial Clerks are trained to communicate via Dreamsleeve – just the mechanics are not talked about or named to outsiders, as guilds protect their secrets. At the same time, Yokuda and Akavir are just far-away places that people can and have travelled to and from, Atmora is known to be frozen in snow and ice (if there’s something else going on there, nobody has come back to talk about it), the Hist are known to just be trees (no matter what those crazy religious natives believe). Magnus might be the sun and the Magna-Ge might be unstars, but they are just nameless holes to Aetherius and their intricate relationship to each other, as well as their names and ideology simply do not matter as far as Tamriel is concerned.

The knowledge about Anu-in-the-Sun is restricted to a handful of people in the entire world. CHIM, comparatively cosmology 101 for Cosmic TES is obscure enough that it drives maybe two dozen people’s lives.

At the same time, these people with esoteric knowledge are among the movers and shakers (or the hidden monsters) of a large continent-wide empire. In this context, Tamriel Rebuilt/Project Tamriel look for the practical implications of esoteric knowledge, as we are focused on implementation.

Morrowind (and Tamriel Rebuilt/Project Tamriel) depict the end of a dreamless, hopeless era which the mainline games after TES III essentially glossed over. 

The continent-spanning empire a regicidal warlord forged four centuries ago with the help of a god-robot of a dead race has been in terminal decline for half its existence, the reigning Emperor broken by years spent in hell at the behest of one of his closest advisors. Pietism, corruption, and adventurism are on the rise as civil order slowly but irrevocably crumbles. Petty nobles are jockeying for positions on top of the waste yard that will follow the Empire’s inevitable collapse, heretical sects preying on the desperate are on the rise, and the Lords of Oblivion are drawn to mortal affairs ever more, sensing the onset of necrosis.

However, these events are not driven by big heroes and villains, but politics, history, and petty, personal grievances. This is the world we want to create, not just as something in the rear window or experienced in books, but something that is visible to the player and can be experienced as part of a coherent whole. Later games have gone in a different direction entirely and the secret, hidden lore of Cosmic TES barely relates to it at all. If it does, it merely laughs at it knowingly, as Jesus does about his foolish disciples in Gnostic texts.

While we build and rebuild various parts of Tamriel, we want to capture that same alien feeling established on Vvardenfell, the same political development, the same internal coherency, the same feeling of history. At the same time, we want to bring new, non-derivative, interesting locales, people, and events into the game.

We are building a setting in which magic is mundane, common descent from the Gods is a plain fact, and history and religion are inescapable synonyms. Sure, we may seem quaint to the other continuities. Outdated even. But Tamriel Rebuilt and Project Tamriel are building a civilization, just as the Bethesda team that made Morrowind would have done.