Ultimately yes. I believe we are talking about when the child is still young,
Does it really matter? And is it really true that folks have as much choice in the first place?
Is a parent who knows nothing about Hinduism going to raise their child in that religion? No. Is a child who grows up in a culture where Hinduism is almost nonexistent and there's no community to support learning about it likely to walk a Hindu path later in life? No.
If you're born in the United States, probability suggests you're going to be born and raised in a Christian tradition. Probability also suggests that given it's a pluralistic and multicultural society, you might convert later because there's a high probability you'll be exposed to other ideas. If you're born in some other part of the world where one religion dominates and there is no multiculturalism or exposure to other paths, probability strongly suggests you're going to be raised in the cultural religion and stay that way. Things are not quite so open ended as we may like to think. At most, we only "choose" within a limited spectrum of what is available and accessible given circumstances. I would say that there is ultimately no choice at all, but spinning up the determinism wheel sort of kills this entire thread, so... let's just pretend we have free will like we usually do anyway.