Cú Chulainn

The expression "Jewish baby" is a categorical blurring. Babies have no religious beliefs. Cutting a baby because of beliefs she or he (or they if intersex) does not hold violates their Liberty. (Catholics are Christians, by the way, whatever extreme Protestants may say.)

No, that's faulty logic. The baby's human rights are inherent, like his internal organs, and don't require his cognition to exist. Religion, like politics or philosophy, requires cognition. Is a baby Libertarian or Marxist, Logical Positivist or Utilitarian?

Indeed the rights of the child, to be fed and sheltered etc. are progressively lost as she, he or they gains cognition and the power to maintain them for him/her/themself.

But religious freedoms should end when it involves irreversible body modifications in blood rituals. Have a party like a Brit Shalom by all means when you name him. But let him decide when he's an adult if he wants penile reduction surgery. He'll still be Jewish if his mom is.