Horses' armor, reins, and bridles experience z-fighting

The Bug:

Horses' armor, reins, and bridles experience z-fighting.

Steps to Reproduce:

1. Summon a horse equipped with a saddle and some armor by using the command provided below.

   /summon minecraft:horse ~ ~ ~ {Tame:1b,ArmorItem:{id:"minecraft:diamond_horse_armor",Count:1b},SaddleItem:{id:"minecraft:saddle",Count:1b}}

2. Mount the horse, look closely at the horse's reins and take note as to whether or not z-fighting can be seen.
3. Look below the horse's reins at either side of their neck and take note as to whether or not z-fighting can be seen.
4. Dismount the horse, look at its bridle and take note as to whether or not z-fighting can be seen.

Observed Behavior:

Horses' armor, reins, and bridles experience z-fighting.

Expected Behavior:

Horses' armor, reins, and bridles would not experience z-fighting.