Considering we have 4 dogs, it would not be a consideration in accepting an invitation.
We do tell invited guests that we have dogs and that they are very friendly and like to greet and play with visitors to our home.
We also warn that if you are allergic don’t visit as 2 of the dogs shed, the others have hair not fur.
We have a large fenced yard, and when we retire to the dining room, the dogs will be outside (weather permitting) or closed into the children’s den.
Here in the country, we’d be hard pressed to find non-dog owners, including the shul rabbi.
That being said, we also have a cat, but she lives in the master bedroom suite and doesn’t mix with guests.
We had one particular acquaintance who refused invitations for years based on the dogs, until last year when we had a week of very hot summer weather and she called my wife and asked if she could attend an all ladies swim party wife was hosting for charity. My wife told her only the one female dog would be in attendance.