... then we would have a case of monkey see, monkey do.
But when we talk about parents 'bring up their children' in a particular belief we aren't talking about some passive observation, we are talking about a conscious decision on the part of the parents followed up by active, direct and directed promulgation of that view within the child.
So parents 'bringing up their children' don't simply rely on passive observation by the child of the parent perhaps going off to church (while the child remains at home) or perhaps praying. If that was all that happened the catholic church would be horrified. Nope it involved all sorts of direct and active engagement of the child in the religion, with the specific purpose of ensuring that the child understands the religion and accepts it. So let's have a look at the kind of things:
1. Expectation that the child is baptised, during which the parents and godparents promise to bring up the child 'in the faith'
2. Expectation that the child attends church regularly along with the parent
3. Expectation that the parents will teach the child about the religion at home and likely teach them to pray, and expectation that the child will also engage in prayer
4. Expectation that the child attends church-based liturgy studies
5. Expectation that the child attends a catholic school
6. Expectation that at the tender age of 7, that the child will have their first communion and will have instruction leading up to this over the previous year.
7. Expectation that the child will, at the still pretty tender age of 14, that the child will be confirmed and again will need to attend instruction leading up to this.
That's what bringing up a child in a particular religion looks like (some of the elements may be softened by the basic concept that is an active direct process remains).
You don't bring up a child to be musical by simply know that dad likes music and seeing that he sometimes plays the violin - you bring up a child to be musical by actively involving them in music, by starting lessons on an instrument at an early age and insisting they practice and don't give up, by expecting them to take exams, by expecting them to be involved in extracurricular music groups at school and outside etc etc.
'Bringing up' is an active and directed approach not a passive observational one.