Disabling Optifine seems to have prevented the mounts from appearing invisible or vanishing, but they still briefly clip through the ground before returning to their former position.
Here is some footage as proof: https://youtu.be/74Bi7xncHtI
It happened again, and I lost my mule. I dismounted it on a mountain and it shifted away under it. I heard it for a little bit, but after tabbing out and relaunching Minecraft there was no noise. I think it fell into the void, poor thing. I'm gonna backup my world and attempt to record the bug, I'll give a link if I succeed. I'm a little frustrated because this glitch has made riding any animals in the game risky or inconvenient. I forgot to mention yesterday that I am using Optifine, I will launch the game without the mod to see if it's the possible cause.
I believe I have encountered the same problem in 1.13.2. When I'm mounting a donkey or horse in single-player survival and sprinting, if I quickly jump off the animal can go invisible or vanish completely.
My first encounter with this bug was when I was mounting a donkey near a roofed dark forest. I got off the donkey to place a bed and sleep because the sun went below the horizon, but after my character woke up the donkey disappeared. I disabled my texture pack-since the donkeys' and horses' textures were broken-to see if it would reappear; still couldn't find the donkey. I exited and relaunched the game, got the same result. Searched nearby trees and still couldn't find it, nor hear it, so I had to spawn another one in (I traveled far from my base to find this animal).
In my second encounter, I was mounting a horse and I was positioned between two cliffs. Just like with the donkey, I jumped off the horse while it was sprinting and it disappeared. By now, I switched my texture pack (one that didn't have broken horse and donkey textures). After tabbing out and exiting the game's window, then relaunching it, the horse reappeared with no further issue.
I have the Windows 10 Home operating system & had Java Version 8 Update 181 [build 1.8.0_181-b13] when this occurred. I have updated Java (now have Java Version 8 Update 191 [build 1.8.0_191-b12]) and will report back here if I encounter it again.
I did search before reporting, but I thought I should still report the issue since it was occurring in another version. I'll keep that in mind the next time I may report an issue, thanks for the quick response!
After further exploration, I discovered that this issue only targeted SOME sheep. Sheep near the spawn point were targeted while sheep located on a farther side of the island weren't and behave perfectly fine.
Another thing, mob's movement in general seem to stutter.
I agree. The biomes also don't transition well, unlike the nether atmosphere ironically, and don't connect properly. Nether wastes cut through every soul sand valley and warped forest; I'd assume that it does interrupt the crimson forest, but I haven't found one of 'em yet in my short exploration in the beta.