I would imagine in this case it is very important. As she said, the no skin to skin is because baby will need wrapping due to the lesion on its spine, probably to to prevent infection and further injury. I assume no putting to breast will be for similar reasons, and because babys head needs to tilt to latch on which may be a problem for the lesion on it's spine/neck.
Some issue's aren't an issue until baby is out and using its lungs for oxygen. Thats why we have so many congenital conditions that aren't an issue until baby is out. A vaginal birth may be advised against but fine, but the second baby takes its first breath its a race against time. A good example is structural heart abnormalities, until its born it doesn't need (or want) the blood going up to the lungs to be oxygenated due to placenta, but the second its taking its first breath its a race against time if the pathways to and from lungs aren't working properly.
It's great people have more options now, but unfortunately when babies are likely to be born quite poorly they're not always in the best interests of the baby, even if it is important to mum. Unfortunately, depending on the severity, in this case every minute OP delays baby going down for an operation could be another minute where either more fluid builds in babys brain and cause damage or a minute of holding baby where the membranes and spinal cord bulging out of the lesion could be damaged. Best chance of baby having as few deficits as possible could be very dependent on how quick baby gets the operation, and how little it's handled beforehand. As absolutely heartbreaking for the parents as that is. All we can do is send as much love and hope as possible.