Adventurers League Player's Guide says, that we may not play characters with the neutral evil alignment:
we’ve decided to restrict alignment choices to keep groups from
becoming too self-destructive. You may not play
characters with either the neutral evil or chaotic evil
alignments in the D&D Adventurers League.
Does it concern only newly-created characters, or is it true for the rest of the game? What if alignment was changed by the DM? Could it be?
Example 1. I've created a neutral character. Later in the game he killed someone, and the DM considered this act as "evil" one. Let's say there were several such acts. Should the DM forcefully shift my alignment to "neutral evil", effectively turning it into an inappropriate one (hence, kick the character out of the campaign)? Or how is this alignment rule supposed to work?
Example 2. A lawful neutral character committed several "evil" acts, and the DM shifted their alignment to "lawful evil" accordingly. However, ALPG says "you may play a character with the lawful evil alignment, but only if you are a member of either the Lords’ Alliance or Zhentarim factions". The character isn't a member of Alliance nor Zhentarim for now. As the result, should they be kicked from the campaign indefinitely? Or how this situation should be resolved?
The 7.0 version of the AL Player's Guide has a slightly different wording:
As an Adventurer's League player, I'm hugely in favor of this. I'm giving up my Saturday or weekday evening to join together and go on an adventure.
The nature of the structured, drop-in format means that these sessions are generally "go through and solve a pre-written module" rather than "it's the DM's world — or the table's world — and any module content is simply a behind-the-screen aid to reduce prep time". This means there's less latitude to explore alternate paths and still, you know, get through to a satisfying end. Adventurer's League modules aren't written with evil characters in mind, and by going against that, you're wasting everyone else's time.
Additionally, unlike a home (or school or workplace or whatever) gaming group, you're not necessarily my friend. In a gaming group, it's important for everyone to be on the same page, but since in public play there's no preexisting social dynamics to work that out, cooperation with the alignment rule is much more important. In Adventurer's League, it's expected that as a team, we're the good guys.
So, if you show up and act out of coordination with that, you're hurting the fun for other people at the table. And since they don't necessarily know you well enough to feel comfortable objecting, they may just have their fun ruined without any real recourse.
In a home game, you might accept the alignment change and then ask for some way to find atonement. In AL, ain't nobody else got time to make this thing all about you.
So, yeah, the appropriate thing to do in example 1 is retire that character from play. Make a new one, and make her or him a hero like Adventurer's League asks for. (Or, as the exception lists, be lawful evil but with a bond which ties you to getting along nicely with others and doing the adventure.)
In example 2 — lawful evil — you could have the added option of switching factions. I don't see any reason why the DM wouldn't allow this. You loose all existing renown and benefits from your current faction, and starting with no reputation or rank it's probably fair for you to not get any in-game faction benefits this session.
The section of the guide on Factions has this further guidance, which underscores my basic point and should definitely be kept in mind if you decide that a faction switch is the way to go:
The only exception to retiring or changing the character would be if you feel the alignment change is unfair — you weren't acting out of an evil impulse, but an accident happened, or something. In that case, talk to the DM and ask to a) not have an alignment change after all or b) accept it for the session, but promise to actually behave and cooperate, and figure out what to do next when the session is done. If you can't work something out with the DM, talk to the organizer.