I endured more than my fair share of childhood trauma. Yet, my adoptive parents presented me in church for baptism and the other sacraments. We attended Mass on a regular basis. We were sent to Catholic school and taught to cherish high moral standards for ourselves and our friends. I rejected this all for over 11 years, but I came to see the wisdom and value in such an upbringing. Now I accept the Christian faith voluntarily, with free will; there is no force or coercion or violence involved.
participation in the rituals is mandatory, lack of belief is not optional, and heaven forbid something fundamental about you cross the line (i.e. try being gay or transgender in a religious household). that little word "inculcate" puts it pretty well - indoctrination by forced repetition. you view it as passing a gift along, some bearing the end of the gift view it as torment
If it involves more then negligible amount of spanking in the "how to train your baby" style or emotional manipulation, it absolutely is coercive.
As in, there is such a thing as healthy amount of teaching your faith. There is also religious based abuse. And then there is someone saying "glaring deficiency of public school is the inability to train your child's character for most of the day" which do suggest overbearing amount of it.
I strongly doubt that. It may have been true at some point, I don't know. It was certainly my stereotype growing up several decades ago. But now that I'm homeschooling and in contact with numerous other homeschooling families, I haven't really seen it. At all.
Other areas could certainly be different. Here, in the SF Bay Area, it's mostly about parents who see their kids just not thriving in one way or another at traditional school, and not really having any effective levers to do something about it while staying within the system. So yeah, there's an element of control, but only of the environment and opportunities available. Especially today, I'm skeptical that controlling the landscape of their peers' opinions is even possible. I guess it is for younger kids, when you could restrict their access to devices for anything but academic purposes. But generally there's just too much stuff to be doing in your own life and setting up and managing the kids' classes and activities—it'd be tough to micromanage their beliefs and values or whatever even if you wanted to. It's not that different from traditional schooling in the end.