We were discussing a principle, that being whose wishes should prevail in this matter. We were not discussing how likely it was that a Muslim ceremony would be performed.
It was you who introduced the specter of a Muslim ceremony. I merely commented as to its unlikeliness. As in, find me one Muslim hospital in the US.
That being said, as to the principle of staff at a Catholic hospital baptizing a Jewish child, I’ll reiterate:
“I would think it highly unlikely in this day and age for staff at a Catholic hospital to baptize a child, or that a dying child would be in the hospital without his/her parents at his/her bedside, except in the case of a severe emergency. In a case like that, an unidentified dying child might be baptized in a Catholic hospital’s ER. But I don’t think Jewish parents of a sick child who take their child to a Catholic hospital have anything to worry about.”
As fate would have it, I have had personal experience taking a critically sick child to the ER at Georgetown University Hospital, a Catholic hospital. The last thing the staff there was worried about was my son’s religion. They wanted to save his life. And did. I was not asked about his religion until he was admitted, and at that it was for informational purposes only, so the clerical team from our (or any patient’s) faith would be advised about which patients might wish their ministry. That is pretty standard protocol at any hospital.