I have put 2 brown mooshroom and 2 red mooshroom in an animal pen outside of my house. I decided to go out exploring, and when I returned, the brown mooshrooms despawned but the red ones were still there. I decided to wait for a thunderstorm again to get 2 more brown mooshroms and named them, ensuring they don't despawn. I also breeded them together to get a baby. But they still despawned after I went exploring and came back. The red mooshrooms were still there, unaffected.

Right when I updated to 1.16.0, it happened again. It also seems that feeding a flower to them doesn’t seem to prevent them from despawning either.