The real problem here is Uber/Lyft not accounting for this in their app. As someone who takes rideshare with a small child who needs a car seat, I've had similar issues.
A person with a dog will need extra time getting in and out, and the driver will need extra time to clean the car and remove any dog hair or other stains or spots. A person with a carseat like myself needs extra time to get into and out of the car while I strap in the carseat. I'm really good at it, but it still takes an extra minute or so to strap in the seat and then strap the child into the seat.
The apps need a way for me to say "I have a carseat" or "I have a service animal" and then give a bonus to the driver for picking me up. Incentivize the driver to want to come get me, and compensate them for the extra time. I'd gladly pay and extra "carseat fee" so that I don't get an unhappy driver who gives me one star just because they had to wait for me.
And in the case of the service animal, they shouldn't have the option to reject the ride and the rider should not get charged extra, but Uber/Lyft should have to compensate the driver for taking that ride as a cost the rideshare companies bear under the ADA.