While it is true that schools have a heavy influence on children, don’t discount the influence of the church. Churches have their own religious education programs, but each church is different. Each church is going to focus on different aspects of religious doctrine and moral guidance. It is impossible for most schools to be so specific, especially in America where we have separation of church and state, so schools cannot teach religion.
Parents do have the option to choose church-run schools, which are often (but not always) specific to a particular church’s beliefs. Parents can also choose blanket Christian schools, for example, that are careful not to choose a specific version of Christianity.
So parents can look for the church that most specifically matches their beliefs, and if they choose and have the financial means they can also send their child to a school run by that church.