Definitely not a thing. They are not good Catholics if they are making up rules like this. The Catholic Church is so dogmatic- and they are adding their own dogma to the mix! I'm Catholic and am very close with a number of priests and nuns- who have come to my house after Sunday mass for meals.
I'm not sure why you can't change godparents...I would in a second if my children's' godparents were making this occasion about them and their weird fake beliefs.