Our group prefers to adopt AL rules for our home games because we feel it starts us off with the right mix of fun and balance (multiclass allowed, feats allowed, rolling for stats disallowed, fixed hp on level up, PHB + 1, no Aarakockra, etc.). We initially thought that Custom Lineage was allowed (as part of the "customizing your origin" rules presented in Tasha's Cauldron of Everything), and only after getting excited about our character builds realized it was excluded from AL play. That doesn't mean it's necessarily unbalanced mechanically, after all, many whole sources and other balanced races are excluded from AL play this season; it seems (not having played AL myself) that they limit it to races that thematically fit the campaign. It does mean that it hasn't been proven balanced either though, it could be in the same boat as Aarakockra for low level play, so I wanted to take a closer look at the actual mechanics myself.
The obvious comparison to make is between Custom Lineage and Variant Human. They share the same language proficiencies, walking speed, lack of armor/weapon proficiencies, skill proficiency, and feat. Custom Lineage has the advantage of being able to trade the skill proficiency with Darkvision, but so many races have that I doubt it's unbalancing. Custom Lineage can also be small (but retain 30 ft speed instead of most(all?) PHB races I've seen which have 25 ft), but I don't see that as innately problematic.
It seems like it comes down to one major question: Is +2 to a single ability score with a feat significantly more powerful than +1 to two different ability scores with a feat, given that players are limited to Point Buy or Standard Array character generation methods? Variant Human is widely considered one of the strongest races, so being stronger would be a good indication Custom Lineage is too strong (and could possibly overshadow other PCs if one took it, and others did not).
The obvious consideration is this enables any character to start with an 18 in their primary ability score (15 point buy + 2 from race + 1 from half-feat), and reach 20 in their primary ability score by level 4. That means better odds of hitting on every attack, better damage on every attack, better AC for DEX characters, better saves for all casters, etc. This difference largely disappears by level 8
*, when a variant human with a starting 16 could also reach 20 in their primary ability score. As such, I'm only interested in looking at levels 1-7 (mostly 1-5, since that's what the Lost Mine of Phaldever-which is our next adventure-is supposed to take you through, but I'm interested in hearing what happens up through 7 as well).
The half-feats introduced in Tasha's seem quite good anyways (Skill Expert seems universally useful for expertise on any class at level 1 in their favorite skill, while fey touched and shadow touched also give great low level spells 1/day for casters), so being forced to take a half feat doesn't seem like a huge cost for the opportunity to start with 18.
While this definitely seems strong, I'm not sure if it's obviously too strong, or just another valid alternative. Going for an 18 in this way means your second best ability score cannot be higher than 15 (point buy 15, no racial or half-feat increases left), vs the variant human who could have 16 in both their primary and a secondary stat and still have a full feat to spend (or even 16 across three stats if they point buy 15/15/15/8/8/8 and use a half feat to bring the third 15 to 16). I don't think I can resolve this question by analyzing the numbers, without the benefit of actual play experience.
Is the Custom Lineage unbalanced to the extent that typical characters with Custom Lineage noticeably outperform other typical PCs at levels 1-7, including other strong-but-AL-legal races like Variant Human, given that all characters must use Point Buy or Standard Array?
I'm primarily interested in answers backed up by direct experience playing with a Custom Lineage at the table, but if there was a source that proved (for example) Custom Lineage was playtested but considered too unbalanced for AL play that would also be interesting.
* Having 20 by level 4 does mean a Custom Lineage could multiclass more freely without worrying about getting the level 8 ASI, but getting into the weeds of specific multiclass builds is probably going too far off-topic. Fighters and Rogues are also different, etc.