CPM 0.6.24a for BTA 7.3_04 does not appear to properly support transparency. Instead of correctly blending transparencies, they completely override anything behind them.

You can see straight through my head in BTA. Here is how it should look using the same model in Minecraft 1.21.8:

Players in spectator will appear completely opaque while their CPM model is active. Note that this player's name and armor are not visible in the first screenshot where they are in spectator mode, which then re-appear when they enter survival mode:

The player should be completely invisible in the first screenshot.

Important note: BTA does support transparency blending on normal Minecraft skins.

I have what I believe is the same issue, however it also extends to the Editor.

In-game, any part of an opaque element occluded by a translucent element will be culled as seen in the following examples:

In the editor, any part of an opaque element occluded by a face of a translucent element will flicker rapidly, as seen in the following example:

One thing to note however, is that if a translucent element is occluded by another translucent element, it will render correctly both in the editor and in-game, as seen in the following example:

Attempting to use this as a workaround, by giving our opaque elements the slightest of alpha, seems successful initially, however anything beyond two layers of translucency causes rendering issues.

In-game with the workaround seems promising with no clipping, however the player in this image is wearing a diamond helmet that is invisible.

Technical Details
CustomPlayerModels 0.6.24a
NeoForge 21.8.31
Minecraft 1.21.8