Mooshroom mushrooms flicker

If you look at the mooshroom mushroom from a distance, you can see it flickering. You can also see that the mushrooms render incorrectly when you include the resource pack.

Steps to reproduce:

1. Enter a world on the 1.21.70.22 Preview.
2. Summon a Mooshroom.
3. Fly 50 blocks away.
4. Use a spyglass to look at the Mooshroom.
5. Observe z-fighting on the Mooshroom's back mushrooms.

This issue is caused by the mushrooms rendering both sides at once instead of only one side at a time. That's why the mushroom in the Pattern Texture Pack screenshot appears to have two stems, both sides are rendering at once.