The Figura mod allows for custom avatars via Blockbench program, that program can create models that are grouped and some groups are Keywords that Figura uses to mimic vanilla behavior. What is broken are RightElytra and LeftElytra keywords that as the names suggest mimic parts of the Elytras when Apugli is loaded.
Figura version that is broken is Figura 0.1.0 Pre-4 to Figura 0.1.0 Pre-6
A Figura report on this that has more specific info and an example avatar can be found here: https://discord.com/channels/805969743466332191/975571425295474708/999759885900206191

I'm genuinely unsure as to what may cause this.

It wasn't the code that you all talked about btw.

It's something else that I may need to dive deep into Apugli to fix.

I'll see when I get the time to see what's causing this.

Should be fixed in v1.9.1