Bug with shoulder-riding mobs of any kind

[middaygardens]

Have you performed isolation testing?
I have indeed!

Describe the bug
Any shoulder riding pets (even vanilla parrots) automatically drop off of the player after a second or two, even if their parent mod adds ways to lock them to the player's shoulder.
Tested most heavily with Lifesize Bdubs's mobs, which are capable of being locked to the shoulder using a slimeball.

To Reproduce
Steps to reproduce the behavior:

1. Install Simply Swords and its dependencies
2. Install any mod that adds shoulder riding mobs (Psittacine, Lifesize Bdubs, etc.)
   OR
3. Tame a parrot
4. Attempt to have the mob ride your shoulder (optional: lock them in place, if possible)
5. Mob automatically falls off after a couple seconds, even without player movement/interaction.

Expected behavior
Mobs remain on the shoulder and are only "shaken off" with the usual vigorous movements like flying or elytra use.

Screenshots
N/A

Additional Info:

• Modloader: Fabric
• Modloader Version: 0.18.4
• Minecraft Version: 1.21.1
• Mod Version: 1.62.0 (most recent)
• Environment: Singleplayer, also LAN multiplayer

Additional context
I've personally not tested it with mods like Psittacine, but after bringing the bug to the Lifesize Bdubs dev, we both took a look and it's something to do with Simply Swords' player entity mixin!
Link to their response about it here, because I'm honestly new to Github and don't know how to reference things directly yet: Superkat32/LifesizeBdubs#2 (comment)