Hope you don't mind me popping in here.
I think if the child is in public school and is focused mostly on sharing their beliefs that it could make them a target for bullies.
I'm not referring to setting an example but by quoting to other students. In an ideal public school situation it wouldn't matter as much. Unfortunately the public schools are not. And in some areas, being religious could make them a target for bullies. Childhood is hard enough without inviting trouble. On the opposite side of that is that if there are a large number of students in the school with similar beliefs they may become the bullies. Anything is a reason to exclude another, strongly held beliefs hurt more then say, hair color.
Some food for thought: It's a two way street. Public schools have kids from all walks of life and if you send you child to school spread their beliefs you can and should expect others beliefs to be shared with them. If you don't want that, then I wouldn't recommend public school. Public schools do not hire teacher based on religion so your child�s teacher (role model/authority figure) may believe the opposite of what you do. If a child goes to school as a missionary this could cause major conflicts within themselves because the person who is supposed to know more has said that they don�t believe that. Imagine being a child and having to come to terms with that. No child should have to.
Is it inappropriate for religious children to homeschool?
I have to say, of course not! If a child is really interested in learning about their religion then homeschooling allows the time to do that. But then I don�t believe religion should be forced on a child. I�m Buddhist but I don�t expect my son to be Buddhist unless he feels that is the right path for him.
I should add that I am against public schooling no matter what! I think the idea that ALL kids learn the same way and are therefore lumped together and taught the same is the cause of a lot of the trouble in schools. I worked at an inner city high school and the students said it was a joke, they weren�t learning anything because the entire class had to follow the pace