In theory it's really no different than eating off plates and drinking from glasses that multiple people have used (talking about both at home and in restaurants.). I mean, those plates and utensils are used by people that are sick, the forks drop on the floor etc.
But, it does seem a little gross to eat off a plate that a pet has licked by dogs/cats especially since animals are know to lick themselves, outside cats are killing mice, some dogs slobber a lot etc. and that seems just gross. But like I said, the dishwasher sanitizes everything.