I'm unsure as to the exact nature of the issue. It was reported on my GitHub as specifically being related to FreshAnimations, entity_texture_features and entity_model_features. Simply put, the custom textures from Lootr are not displayed, and it instead defaults to using Vanilla textures.
Unfortunately, the user hasn't provided any further information about what version they're running on, apart from it being Forge. However, from looking at https://github.com/Traben-0/Entity_Texture_Features/blob/master/common/src/main/java/traben/entity_texture_features/mixin/entity/block_entity/MixinChestBlockEntityRenderer.java, it appears as though this mod mixins in to the default block renderer.
This is the class that Lootr extends which is what the Lootr renderer extends: https://github.com/noobanidus/Lootr/blob/1.20.1/src/main/java/noobanidus/mods/lootr/client/block/LootrChestBlockRenderer.java
I've been quite lazy in my implementation, simply overriding the getMaterial call and relying on the logic injected by Forge to handle the material. I'm not entirely sure how your mixin system handles this and thought I'd reach out and ask if you had any suggestion on how to properly integrate with your mod.
The "simple" solution that I considered (simply not extending the default ChestBlockEntityRenderer) would seem problematic because that would then prevent the "use Vanilla textures" configuration option (a part of Lootr) from functioning the same way as then it wouldn't have your mixin applying.