I'm making a teifling based on the Levistus Variant, and l wanted to make a public copy that was just the L-Teifling, but updated to match Tasha's/MMotM, but Armor of Agathist ruined that plan (Cause it's not from the Basic rules, thus l can't share homebrew that has it).

However, the weird thing is, l can't seem to be able to copy this race. I thought I might be able to just create a copy by pressing a button beside the Delete button, but it wasn't there (and doesn't look to exist), but l know l saw homebrew races in the "Create Race" options, but l couldn't even find my Teifling there. What's going on? Is AoA ruining this too?

The Levistus Variant is there:

Three things:

1. In order to make a variant Tiefling based on the Levistus Variant, you must own a license to that variant from DDB. If you have a License to it then check that your Account Entitlements are in sync: (https://www.dndbeyond.com/account/marketplace).
2. Homebrewed Variant Races are not available for use as templates to make further homebrews.
3. Even if you made your variant based on the Levistus Tiefling, it would be against site policy to publish it and the Mods would eventually just take it down anyway.

1. I Do own it, and my homebrew was copied from it, then modified.
2. I See, that must be the issue. Do you know why that is?
3. Why is it against site policy? It's homebrew, and that's allowed, plus it's legacy content that's unavailable on the site now that MMotM is out and the book it came from is not able to be purchased anymore, so it's not like WotC/DDB is losing any money from someone homebrewing a version of a outdated race to have the modern "Choose your languages and Racal ASI's". 

It's a moot point, since it has Armor of Agathist, which isn't in the basic rules, and thus can't be shared anyway, but I'm curious.