Based on that reasoning I should be a Lutheran. I think you fail on that reason.
This doesn't mean you're not correct on the other two, though.
Of course, there is always the maxim “Never attribute to malice that which can adequately be explained by stupidity.” I guess we just live in interesting times.
According to the teachings of ISLAM, if one’s father is a Muslim, then the child is a Muslim. If the child converts to another religion( (of from Sunni to Shiite), the child is a heretic, and is to be put to death.