There is a lot of 'fanon' which is generally accepted by the audience, such as dates and times of events or character back stories, in leiu of any actual on-screen evidence establishing different. I can understand why we do this. Especially in terms of TOS, these kinds of details were never fully established in any linear form. There are gaps in where characters come and go, whether they were aboard all along or only transfered there later (hello Chekov!); the dates and times that these events take place, like where The Motion Picture stands in relation to The Wrath of Khan; and so on. Later spin-off shows were produced at a time when continuity mattered just a bit more, so in those cases a lot of these fine details were actually filled out on-screen. All the same, there are always gaps.
Fandom has of course decided to fill in these gaps with their own theories. This 'fanon' is naturally often seen as being better than nothing, and in some cases there's a kind of general consensus about certain things where the 'fanon' has transcended its roots and become firmly established as being the 'correct' view. And even though it might never have been established on-screen per se, for the lack of any better explanations a lot of us find ourselves more than happy to accept this kind of 'fanon' as being fact. Even the Star Trek Wiki, Memory Alpha, contains articles which play fast and loose with the distinction between fanon and fact (Memory Beta is of course even looser still).
IMO even the Okudas, who actually came the closest to canonising a lot of this stuff, really only ever peddled a commerical form of 'fanon'. Their views held more water as a result of them being part of the on-going production team. But what is oft forgotten is that much of what was published in the Encyclopedia and the Chronology was really just higher profile 'fanon', rather than Canon. Even the Okudas themselves admit that a lot of what they wrote was simply conjecture on their part, and some things that they 'established' got debunked in subsequent episodesbut. But again, for a lack of better explanations, many of us are happy to accept what they said as being a general rule of thumb. I suspect this is because we all need to have a common ground on which to talk about events in the Trek universe.
On another tangent, sometimes when a later Trek series like Voyager or Enterprise broke the conjecture that we fans had already accepted as being 'fact', the producers would be accused of contradicting the established continuity... even though more often than not that continuity had never actually been established on-screen in the first place! Is it possible for the series to contradict something that was only ever the purview of fan conjecture? It would appear that the answer is: sometimes it can.
My question is therefore: do we as fans sometimes accept this 'fanon' too readily as being firm 'fact'? Should we instead be questioning and debating these so-called 'facts' more strongly? Or is the use of 'fanon' a crucial tool in our understanding of the Trek universe? Do we need to have this kind of firm foundation in order to help us all join the dots together?
I think fanon is okay to a degree, like an author uses their own ideas of fanon in a fanwork.
It can become something else entirely if said author tries to push that idea off into the fandom like they are right and anybody else who writes or draws otherwise is wrong.
Sometimes a fanon "thing" ends up picked up by the entire fandom, and that's fine too. As long as nobody pushes their personal fanon in other peoples' faces like it's established fact, I don't mind it at all.