> do not want Rebbeim to influence their children, just to teach them.
not all, but some Rebbeim in a Litivishe school were influencing my kids to use “modern” as a generic swear word for everything they disagree with, as some do it here. To borrow your words, “This lack of respect for religion rubs off on the children.” When we went online, kids kept the middos they learned, but stopped swearing.