Are the societies meant to be secret? I don't think they are.
The Harpers are explicitly secretive. I often see Zhentarim members play their faction affiliation as, if not secret, then not something they want to be overt about.
As I understand it, the general crux of how the adventure league works is that within the world there is this job known as "Adventurer" and they are organized by guilds.
They're not guilds so much as... well, factions who want to advance different agenda. "Guild" implies a professional organization that provides training and employment. Factions don't do that. You could count "going on an adventure" as "employment" here, but since those same employment opportunities would be just as available to a factionless adventurer as they would be to one who's part of a faction, it doesn't really seem relevant. The only thing you really gain out of performing duties for your faction is increased standing in your faction, which, y'know, doesn't exactly pay the rent.
This helps neatly and easily explain how and why you can sit 5 random characters down for a random adventure and they can all be considered hooked and ready to engage with it. No session 0 every play session.
There wouldn't be a chargen session anyway. It's a series of one-shots. Strict continuity about how we met, etc. is totally unnecessary.
In order to gain membership into this guild, one needs to be vetted and doing so is done through these organizations who then sponsor the person.
Who's vetting your 1st-level PC who's chosen a faction, then? No one has to give you permission to be in one faction over another. The only that matters is your interest and your PC's alignment.
Now, if when you are making your character one of the first things you say is "I am a special snowflake lone wolf, screw all authority and organizations and affiliations. I do whatever I want whenever I want and all of those factions can go screw themselves if they think I'm going to follow anyone else's agenda!!" which is certainly what it sounds to me one is saying when they just outright reject the idea of working for any of the main organizations....
Yes, let there be no middle ground.
Well, if one has such a major problem being associated with a distant organization who don't really enforce their agenda and with whom membership provides only benefit, how exactly is that going to work with a much closer organization with people whose actions and direction are going to immediately affect where you go and who you talk to and how you relate to NPCs and the general choices you make?
Because not all factionless PCs are sociopaths.
What is the first thing this special snowflake lone wolf who tells all organizations to go screw themselves
I'm not telling anyone anything! It just seems to make sense for my character, in light of his backstory, that he's not part of a faction. You make it sound like every new PC has to run through a career-guidance seminar put on by representatives of the five factions. On the contrary, it's totally conceivable to have led a pre-1st-level life that involved no contact with the factions at all.
Of course they aren't going to stay with them. Why would they? If not metagaming and actually playing consistently, they are going to turn heel and abandon the others at the first opportunity they get... or when everyone else goes left, they will go right on their own because that's what they want to do and, as a special snowflake lonewolf, what they want to do is what they do and no one is going to tell them otherwise.
I don't understand why you're so determined to make out factionless PCs as being so anti-social. It's like you're equating it with the old notion of Chaotic Neutral -- the old "do anything anytime for no reason" canard. You seem to have a real axe to grind, and I don't get why.
My factionless PC is perfectly willing to work with other PCs who have similar aims, but that doesn't mean it's ridiculous for him to not seek out and apply to be a member of a faction.