I guess my answer would be BOTH!!!
I think it is the parents responsibility to prepare their children for life in general by teaching them the best moral ground & the best way to relate with others. Schools should give them the knowledge with which to survive life especially in the workforce. I found school another good place to grow socially.
IF a child learns something at school that is opposite of the parents belief, then I feel it’s the parents responsibility to use that opportunity to explain to the child WHY they feel it is wrong. So, nether should be the ONLY experience the child receives; but BOTH working in tandem should give the child a well rounded start on life!!!
The reality is that the child will determine their best course in life without listening to either thw parents or the school. Given a good foundation, the child will have a better chance of choosing te right course in life!!!