If you had a dog...

If all attempts at training failed and there was no way to keep him/her outside, yes.

Probably not, but I'm very sympathetic to animals (we have a cat who routinely pees on our stuff, and is pretty neurotic in general and she's managed to avoid being shipped out). Why not just close a door, make sure the toys are stowed securely out of the dogs reach, and try further training first. A situation like that would be frustrating for sure, but not necessarily a deal-breaker for me.

I would try keeping him/her out of my room completely. If I couldn't do that then I would make sure he had a good home to go to.

Nope. Much as I love toys, an animal friend is more important. If all attempts at training failed (and I'd be super persistent about it), I'd just be sure to keep my toys behind closed doors.

if the dog mouthed them in a sensual way while devouring them I'd probably record him doing it and post it on youtube

I would probably try and come up with a different solution of storing them, such as keeping them in a box on the top shelf of the closet so the dog wouldn't be able to reach them.

Honestly im not really an animal person to start with so I wont have a dog but if I did and that happened idk if i would get reid of the dog i would be pissed though.