What effect do illness and/or disability have on parenting?
Illness and, in particular, disability do not have to have any impact at all on parenting. That is, a person who is ill can still be a wonderful parent (or a terrible parent). The same is true of a person who has a disability. (Of course, there are some illnesses or disabilities that are so debilitating that they could prevent a person from parenting, but I assume that this question is not asking about these conditions.)
All of the important parts of parenting do not depend on physical ability. Parenting skill does not depend on the parent’s ability to run around the playground with the child. It does not even depend on the parent’s ability to do something as basic as hearing or even seeing the child. Instead, it depends on the parent’s ability to show that child that they care. It depends on setting limits for the child so that the child learns how to behave. It depends on making the child aware that the parents want nothing more than the best for him or her. Any parent who can get these ideas across will likely be a good parent, regardless of whether they are blind, or deaf, or have Parkinson’s or cancer.
That said, disabilities and illnesses can make parenting difficult. Parenting is a very difficult job that demands that the parent be able to keep control of their emotions. Parents have to be able to respond in the correct way in a variety of situations that can be very stressful. Illnesses or disabilities can make this more difficult to achieve. A person who has a serious illness or disability might often be stressed simply because of their condition. This may, at times, make it harder for them to retain the sort of control that they need and want to have.
Thus, disabilities and illnesses can make parenting more difficult, but they do not prevent a parent from doing a good job of parenting.