seems like the mod may cause horses to not poop if they are locked?

Not directly. Horses not pooping can be caused by them not decaying.

Could this issue be caused by the vehicle decay protection plugin?

I’ve been turning off plugins but I’m still unable to determine the cause of the inconsistent poop drops. Sometimes I log in and have 1500 in the hopper, while other times there’s nothing at all. I disabled the cupboard no decay plugin, but I still don't get any poop. It seems to work occasionally when I turn off the vehicle decay plugin or vehicle deployed locks.

This is cause by vehicle decay protection. They stop eating becaue decay stops. They don't eat, they don't poop.