I think, that is true in Russia too.
In my opinion,
Заткнись — totally unacceptable
закрой свой рот — rude (something between acceptable and unacceptable)
Закрой варежку! — totally unacceptable
Замолчи! — rude but acceptable
Довольно! — polite or neutral, bookish
Попридержи язык! — a bit rude, bookish
Слушайте внимательно — polite or neutral
Слушайте! — neutral
Молчать! — neutral or rude but acceptable depending on the situation
Молчи! — neutral or rude but acceptable depending on the situation
Молчите! — neutral or rude but acceptable depending on the situation
If it’s useful for you, I can think of some other similar phrases:
хватит! ‘enough!’ — neutral
тихо! ‘silence!’ — neutral
тишина! ‘silence!’ — neutral
прекратить разговоры! ‘stop talking’ — strict but not rude
минуточку внимания! ‘a minute of attention’ — polite