A vanilla Elytra equipped in the cape slot does not use custom elytra models when present in the Custom Player Models mod.

1.20.1

Fabric

I should note that a similar thing does work in the Origins mod, so I do know it's possible.

(Matter of fact: having it equipped as such while being an elytrian results in z-fighting copies if the model is similar enough to vanilla.)

Trinkets does not add support for elytras and is not responsible for this.