Yes, I believe that it is justifiable to eat grey squirrels, because they were put on the earth for a reason. Also, there are plenty of squirrels in the world. The ecosystem is not going to fall off balance if a few of us eat a tasty squirrel. If God didn't want us eating his creatures, he shouldn't have made them so tasty.
I do not see anything wrong with people eating grey squirrels. It could be a good source of protein. The only problem I would have with a person killing an animal is if they didn't do it humanely and didn't do if for the purpose of food. I think that there is not anything wrong with it.
In more rural areas this for some is a form of nutrition, while it's weird to a lot of the country I don't have a problem with it. If somebody is blasting squirrels just for the amusement of it that's an issue, but if they're actually consuming the animal then that's just hunting for a purpose.
It is justifiable a to eat grey squirrels. They are not domesticated and some people will need to eat suirrels because they can not afford to buy food at grocery stores. This will mostly occur in rural areas in the south and not in big cities. This could happen rather soon.
I do not think it is justifiable to eat grey squirrels. There are a lot of them roaming around and there are hunters who specifically go after them at a certain time of the year. There is nothing wrong with hunting them. I just personally would not hunt or eat them.