On DogVacay, I was able to list some breeds that I didn't want to accept. I can't find that option on Rover, is it there?
As someone who has been doing this for over 20 years and also being an animal trainer and behavior modification therapist for animals, someone who has trained, competed, bred, boarded, rescued all sorts of dogs, I can tell you that breeds are not so much the issue as to the energy type, the personality, the level of obedience, the amount of socialization and the age, those things will have a whole lot more of impact on how the dog does while in your care than the actual breed of the dog.
But of course if the area where you live has breed selective legislation or if your building by-laws or insurance company have breeds they do not accept, that is a whole other thing.
That was an awesome option on DogVacay, as it just removes any awkwardness for the sitter. I find Rover does not make improvements to the web site based on sitter feedback, and too often the reply is "put it in your profile."