I'd be very unhappy about it. Much as I'd be quite unhappy if she had a leopard or a werewolf in a pen in the garden.
I don't like dogs, & I REALLY don't like Staffies. MIL had one, which dh adored, & which was the cause of some tense marital moments re: dh & my diametrically opposed attitude to the dc being anywhere near the bloody thing.
The dog never put a paw wrong, incidentally, it just happened to be a big ugly dangerous looking bugger from a breed with what can only be described as form...
& you probably think I'm totally BU, which is fine, but irrelevant - it's for the parents to say if they're OK with it or not.
If my CM got a dog, it would be a whacking great minus, I'd be very inclined to place the dc elsewhere, & she could think I was being as silly as she liked.