Babies are actually different from adults here; they get antibodies from breast milk and it supports their immune system, since theirs isn't developed. It's a good thing.
The mRNA used in the COVID shots isn't normal, of the type found in the wild. It's been created in such a way that the immune system doesn't recognize it, and then wrapped in artificial lipids. So you can't generalize from natural mRNA molecules to the artificial types, they are fundamentally different in both construction and effect.
This is not at all the same situation, and this sort of hubris is what causes public health disasters such as the Vioxx, Thalidomide or Dengvaxia scandals.
This is artificially created genetic material ending up in newborns after the manufacturer assured the public that was not possible.
I consider this incredibly serious.
So the question is if it harms them, which this paper says it doesn't, and the mRNA vaccines are approved for infants already.