The mod (1.20.1 as far as I know, but probably later and earlier versions) is incompatible with the SkinShuffle mod. The game crashes once the main menu screen is loaded. SkinShuffle and Wildfire's Female Gender mod are the only two mods installed.

The crash log is posted here.

Here is a video representing the problem:
https://github.com/WildfireRomeo/WildfireFemaleGenderMod/assets/83091369/773a4ee1-9e7d-4a23-b4cd-a6a4b57f9245

Currently using Skin Shuffle or Skin Overrides on MC 1.21.4 with mod version 4.3.3 doesn't create any issues. Also, 2 weeks ago I tried Skin Shuffle on MC 1.21.3 and it had several model errors, but nothing related to FemaleGenderMod, so with older versions, like your case, 1.20.1, I guess these are issues that are fixed exclusively for the latest versions. And this is done by many developers, like for example Sodium creator jellysquid3 or C2ME creator ishland. And I could give you many more examples. Simply put, your mistake wouldn't be WildFireRomeo's responsibility, so try to update your MC. I understand that not all mods are updated quickly, so the only thing left for you is to wait. I'm still waiting for several mods, among them the legendary Dynamic Surroundings!

Merry Christmas!