Although the mod is denoted as version agnostic from 1.8 through 1.16.1, versions of Forge after that point now include a mandatory requirement that the mod include a "license" key in its mods.toml file that specifies the licensing information of the mod. If the mod excludes this information, it cannot be run.

I presume that CustomSkinLoader works just fine even on 1.16.5, but the absence of this line prevents it from running with a hard crash. Utter genius on their part. ...And they wonder why Fabric is gaining popularity. Hah.

[edit] Ah, I was running version 14.12. This may have been resolved in the latest artifact. I'll double-check against 14.13.

Closed issue as already fixed in 14.13.