Yes but they shouldnt, humans like new and wonderous things, and because it was from outtaspacee people would be like, Ooooh how Dare you injure it ect, yet theyd put down earth dogs, theyd hunt it keep it care for it, just Overall pay it more attention good and bad
If aliens came to us first, we would know they're more technologically advanced than us. Even if the 'dog' was not, if the Aliens are more intelligent than their human equivalent, surely this means their 'dogs' could be more intelligent than our dogs?
It is not to say we'd respect them more, but certainly more different. It would be unfamiliar to us to give an alien dog a belly rub as it's abnormal; quite like if you were to give a belly rub to e.g. a duck.
If this said dog did come to our Earth, I do believe at first we would be treating it with more respect because we don't know what this sort of dog could do nor are we familiar with it. I mean you wouldn't want to harass this creature or try to make it extinct, would you? You would want to learn more about it and understand it more. However as we got more familiar and learned more about this animal, then we'd be giving it the same amount of respect as we give to our other animals.
The idea is that this creature would be interesting and new to us, but with the same intelligence as dogs or the like. Is it inherently wrong that they should be treated better than our own earthbound canines? Or should the question ask if the aliens brought a creature identical to a dog?
When that alien dog is first sent to Earth, people would be amazed, surprised, and shocked. They will try killing them and avoiding them.
But, as time passes on, this creature would soon be integrated into our world and would be no different than a dog as we will accept it in the animal kingdom as another species.
There is no way we can possibly predict with significant how we'd treat other species' pets as our treatment of them depends entirely on the nature of such a pet. If the creature were exactly like a dog, we'd treat it like a dog. If the aliens who owned this pet were millions of times more advanced than us there's no telling what their pets would be like and therefore no telling how we'd treat them. This question is riddled with problems.
There has been tons of racism throughout history. Why? Because people are afraid when they see something different. If aliens invaded earth, forget the dogs, people'd kill every alien they see. These animals would be like bugs, people would think they're ugly and kill them. I don't think it would be a good idea for aliens to bring their pets to earth, because we'd kill them out of fear.