Hello, there's a lot of different answers out there on Background rules (especially since the rules have changed over time) so I thought I'd spell out the rules on Backgrounds here. There's 3 parts to this: A) parts of a Background, B) the rules, and C) my interpretation of the rules. Documents not yet updated (or are just pure legacy) for the current season are noted in red.

Parts of a Background:

• Backstory: This is the flavor of the background, which helps bridge the gap from your origin to your path down adventure-alley.
• Skill Proficiencies: Limited to 2 and generally compliment the Backstory.
• Languages and Tool Proficiencies: Combined, these are limited to 2.
• Characteristics: Most backgrounds have 2 Traits, 1 Ideal, 1 Bond and 1 Flaw. Its all flavor.
• Feature: A tangible in-game benefit that comes with the Background.
• Equipment: Usually a combination of items and gold. These are in addition to your Class starting equipment

Rules {The PHB language superseded by Adventure League language is shown with stricken text}

• PHB, page 125: "Customizing a background: To customize a background, you can replace one feature with any other one, choose any two skills, and choose a total of two tool proficiencies or languages from the sample backgrounds. You can either use the equipment package from your background or spend coin on gear as described in chapter 5. (If you spend coin, you can't also take the equipment package suggested for your class.) Finally, choose two personality traits, one ideal, one bond, and one flaw. If you can't find a feature that matches your desired background, work with your DM to create one."

• Adventure League Player's Guide, v 9.2:
  • "Step 1: Choose a race and class: Forgotten Realms characters can choose race and class options from the Player’s Handbook and one other resource—a rule called “PHB+1.”
  • "Step 3: Describe your Character | Background: Choose or create a background using the Player’s Handbook or other campaign resources. Additional resources are permitted in the Adventurers League Content Catalogue (ALCC)."
  • "Step 4: Choose Equipment: Your character’s class and background determine equipment and gold; you don’t roll for starting wealth."
  • "Step 5: Select a Faction (Optional): Your character can be a member of a faction only if they have the Safe Haven background feature (Faction Agent background, Sword Coast Adventurers Guide)."
  • Character Rebuilding: You can rebuild your character prior to playing their first adventure as a 5th-level character—changing any of your character’s statistics but their name and season. Non-mechanical aspects of your character such as alignment, gender, choice of deity, or personality traits can be changed between sessions regardless of level. Your character keeps any rewards and equipment earned to that point. If your character’s class or background changes, they lose any equipment that it granted, along with the proceeds from selling it..."
  • Renown Item: Adept characters can choose to gain a +1 weapon, +1 shield, +1 rod of the pact keeper, or a +1 wand of the war mage tied to their background (a Folk Hero might get an old +1 greatsword that belonged to a retired adventurer, a Sage may find a +1 wand of the war mage hidden in a library, for example). Your character’s Magic Item Limit applies to this item, and the item can’t be sold or traded, but can be replaced with other items as you wish.
  • Faction Membership: Your character can join any faction they meet the requirements for (for example, members of Bregan D’aerthe must be drow). You can only be a member of one faction at any time and maintaining membership in a faction requires a character to possess the Safe Haven background feature (Faction Agent background, Sword Coast Adventurer’s Guide). Your character can leave their faction at any time. To do so, they replace the Safe Haven background feature with a new one or choose a new faction. In either case, they receive a short-term suspension from renown benefits.
• Adventure League Frequently Asked Questions, v 9.1: "Skills & Backgrounds | Custom Backgrounds: You can create a custom background for your character by following the rules in the PHB, but you can't create custom background features." There's also more discussion in the FAQ specifically on exotic languages.
• Adventure League Content Catalog, v 9.01: There's different background rules depending on the season, read that season's background rules if playing a specific season (vs season 0 or CCC content).
• Adventure League Dungeon Master's Guide, v 9.1: "Acolyte Background. Characters with the Shelter of the Faithful background feature can request spellcasting services at a temple of their faith..."
• Sage Advice (v2.4): Can you have more than one background? No. You can have only one background. It establishes key aspects of your life before you embarked on a life of adventure. If none of the backgrounds available matches your character concept, talk with your DM and use the guidelines on page 125 of the Player’s Handbook to customize your own background.
• Adventure League Faction Guide, v 7.1: Does not addresses Backgrounds.
• Detect Thoughts, v 1.4 (Season 8): You can rebuild your character itself, but not its equipment (save for starting equipment granted by the character’s class, if changed).
• Renown Benefits, v 1.01 (Season 8): Legacy document - discussion moved to the AL Player's Guide.

My Interpretation

On Source Restrictions: The background rules do not have the +1 limiter. Background rules are in a separate paragraph, not a sub-paragraph of race/class.  Pick a background from any acceptable AL source. So:

• Backstory: Edit freely. 
• Skill Proficiencies: Limited to 2, pick any.
• Languages and Tool Proficiencies: Limited to 2 total, pick any.
• Characteristics: Pick from any AL-legal source: 2 Traits, 1 Ideal, 1 Bond and 1 Flaw.
• Feature: Pick one from any AL-legal source. Once a feature has been chosen, it can be replaced at any time/level with SCAG's Safe Haven background feature. Additionally, the Safe Haven background feature can be replaced at any time/level with the character’s original background feature (at the consequence of loosing renown).
• Equipment: There's nothing that allows a player to change defined equipment/gold from an existing Background, but everything else can be edited with the above rules...a player is required to pick a defined starting equipment & gold option (but again, from any AL-legal source). You loose background equipment if you change your background. It doesn't specifically say that you then gain the new background's equipment, so I'd say that's at DM-discretion at this point.

Let me know your thoughts, including errors, omissions, or misinterpretations.

Sounds good except:

"Once you pick your background, you can change out the background feature at any time, at any level, with SCAG's Safe Haven background feature...or remove your Safe Haven background feature at any time/level and replace with any other background feature (at the consequence of loosing renown)."

The text you cited says you can swap to safe haven whenever you like but you have to swap back to whatever feature you had before choosing safe haven unless you didn't have a background feature.

true, fixed. thanks

updated for season 9