In filling out the application to take a new animal, the rescue group asks for information for my current veterinarian. Why do they want that information and what will they ask/tell my veterinarian?
First we want to know that you have thought about your pets medical needs. And your vet probably has a pretty good idea of how you treat your pets. Do you bring them in for regular check ups, get them vaccinated, and provide heartworm prevention treatment regularly? When they come it are they clean well groomed, and not showing signs of neglect? Your vet is probably not going to tell us all of that but the vet may be able, based on that information, judge if you treat your pet decently or not. When we call we hope that the vet will let us know that he sees your pets regularly and be comfortable with your adopting another pet.
I have never had a vet tell me that someone would not be a good choice to adopt, but I have had one say that he did not have an opinion. That was not necessarily a problem but it did lead us to investigate deeper. But a good vet reference goes a long way towards comforting us that you will be a good pet parent for this animal that we have invested time in rehabing and saving.
If you are adopting from a breed specific or species specific rescue the goal may be to see if your current vet specializes in the pet you are considering adopting. A breed or species specific rescue is going to know who the best vets in the area for addressing the special needs of your new pet.
If your current vet is not one of the local vets who specialize appropriately, they will likely suggest an alternative. This is particularly true if you are adopting a special needs pet.