Honestly -
When one gets down to the bottom of this, the only real difference between the dog and any other dinner involving meat is tradition.
In other locations with other traditions, dog is on the menu every day - and there are places where things on our menu such as cow, pig, & shellfish are verboten.
So, yeah - barbecuing a dog has a definite 'ick factor' here. But it isn't any more 'wrong' than eating any other animal- unless there was cruelty involved in putting it to death, but that is another story.