In Japan, washing before getting into the bathtub is a cast-iron rule.
Washing thoroughly before taking a bath is a non-negotiable rule in Japan
In Japan, removing your shoes before entering the house is a cast-iron rule.
「鉄の掟」= a cast-iron rule / non-negotiable rule
「湯船に浸かる前に体を洗うのは日本では鉄の掟です。」= In Japan, washing before getting into the bathtub is a cast-iron rule. / Washing thoroughly before taking a bath is a non-negotiable rule in Japan
「玄関で靴を脱ぐのは日本では鉄の掟です」= In Japan, removing your shoes before entering the house is a cast-iron rule. / It is a cast-iron rule in Japan to take your shoes off before entering a house