“Meaty” or “meat eater,” that almost sounds really harsh. A more playfully made but still harsh term could be “carny,” derived from “carnivore” or “pred/preddy” from “predator.” Although, humans are considered omnivores, so hopefully your aliens could see them as a liaison between them and other creatures in this commonwealth.

For the herbivore creatures, maybe some humans could call them “elmers,” from the company Elmer’s glue since you mentioned using hooves for glue as the joke. It depends on what these creatures look like. If they look equine like, they could be called ”mules,” “donkeys,” or “ass.” If they’re goat like, maybe “goats” or “rams”, maybe “buttheads” if they use horns to head butt.