Because I do not support the repression of free choices or a parent's right to smother their child and force them to their own beliefs (Hitler did that to the Germans, anyone who moved to America all those years ago, to the Native Americans both of which ended in mass murder) I would say that it would be none of the parent's business. I'd be proud that my child felt confident enough in me to confide in a life changing experience such as that.
Nobody has any right to turn away their child. Nobody. It just makes them an evil narrow-minded (which most religions are anyway) who has let their religion blind them from what is real.
If somebody in this situation would turn out a child if they converted, they shouldn't have children, simple as.