As long as the dog in training has a vest or other form of identifying them as a service dog in training they should have similar rights. As they are not fully trained and certified, they may be turned away or need permission in some places, especially in schools, hospitals, and work places. It would be a good idea to alert a public place like a zoo, historical place or any area where pets are not allowed. They should be willing to allow a service dog in training, but they do like to know ahead of time. Some organizations that train service dogs have group outings to these places.