The issue for the christofascists isn’t that children are being indoctrinated in school. The issue is the deprogramming of the indoctrination to fear, hate, intolerance, and self-loathing that they get at home from their parents and at church from christofascist leaders.
Schools don’t make people more liberal, exposure to reality makes people more liberal.
I’d rather see two center-right and left groups debating policy rather than needing to entertain the far right policies that many conservatives are fine to be in bed with.