I can't say for sure. I'm sure, like any mother, I would be devastated to have an ill child at first. As to how much damage would be done at that point and irreversible... hard to say.
The much more likely scenario though is a false positive and a breastfeeding relationship ruined. How would I feel about that? Angry. Devastated.
All choices carry risks. I think all parents should be informed of all risks of ALL choices they make involving their children.
Or, if you have a pushy doctor, use this as one of your interview questions and change doctors.
FWIW I'm not trying to use scare tactics. It is incredibly unlikely that a child will have one of these disorders, since they are so rare. Even if you refuse testing, your child will most likely be fine. But there is no benefit to not having the test (again, as long as you have made sure your doctor and yourself understand what the screening is) and there is a risk. The symptoms that show up with PKU, and some of the other diseases are caused by brain damage that is not reversible. That can be the first sign that you need to get your child checked out.
So it's very, very unlikely, but it's very, very dangerous if you're one of the unlucky ones.