Please, non-believers, spare us your wisdom and common sense, thanks.
You don’t even quite understand what Baptism is, and if you did, you wouldn’t believe in it anyways. We have known what it is with certainty for two thousand years.
Surely if it was a matter of a life-saving vaccination or other medical treatment, you’d speak differently, for I am sure even in your disbelief of an afterlife or a God you would still reject relativism as far as to concede that one should do all that is possible to keep the baby healthy and alive.
So please, if you have no better comment than it’s not a good idea, I would be soo mad, consider the risk, etc. there’s really no contribution coming through, just secular common sense that we are all well acquainted with. The OP wants to know what the position and teaching of Holy Church is on the matter, and that is what Catholics have tried to explain above.
I will only add that the matter should be discussed by them with their own priest, who can counsel them on how to bring the matter to the attention of their son.