Is there such a thing as a Christian or a Muslim baby?

Any person who was born on this earth is born into a certain culture. That culture involves a set tradition, a historical background, an ethnic identity, and a religion. This means that babies are born into certain religions, and don't get to choose themselves what religion they want to follow. For example, if a baby who's parents are Arab and Muslim is born in Saudi Arabia, that baby is considered as Muslim from the moment it leaves its mother's womb. If a baby is born in a christian family in the Rome and is baptized, that baby is automatically Christian. However, being born or thrown into something doesn't always define one's belief system. Examples of this are observable when people convert to other religions. For example, a born Christian can convert to Islam, and vice versa. Nevertheless, babies have defined religions from the day they come into this world, as they are baptized or accepted into the religion or are put through whatever ritual their religion requires. So, babies can be classified as Muslims or Christians, even if they didn't choose their religion.

Being born into a religion doesn't necessarily determine one's belief system. One's choices define that person's belief system. Indeed, children and teens may forced by their parents to follow a certain religion, but once those teens become adults, they have the freedom to choose whichever religion or belief system they like. Most religion tolerate conversions, and if one is willing to embrace another religion, then it is that person's choice, and that is what defines that person's belief system. This is the case especially in the three monotheistic religions; Islam, Christianity and Judaism; as they all believe and follow the same God, a God who tolerates a believer to convert as long as that person truly believes in God.

There is a distinction between babies when talking about their religion, and that is because they were born into their religion. Some people consider this wrong, as they take away a human being's right of choice. However, the human being in question here is a baby, and babies do not have developed enough brains to make rational choices for themselves. That is where the parents intervene. They define the baby's religion, and because parents know what's best for their kids, they believe their religion is the one their baby has to follow.