Are there English proverbs that warn against “speaking up” in front of people?

Solution 1:

There are many such idioms, not so many proverbs that I can think of.

Maybe the most famous proverb on keeping silent is from Proverbs 17:28:

Even a fool, when he holds his peace, is counted wise: and he that shuts his lips is esteemed a man of understanding.

It's repeated in various parts of Scripture in different phrasing. I think it's the basis of the familiar

It is better to be silent and be thought a fool, than to speak and remove all doubt.

The following is attributed to Confucius:

Silence is a true friend who never betrays.

In addition to the idioms @Dan Bron mentions, there is also flying under the radar, originally meaning avoiding detection, but now meaning avoiding negative attention as well.

However, even wise people often embrace silence, and there is a saying in teaching that no question is a stupid question. How can one learn if one doesn't ask questions?

Solution 2:

We stole the proverb from you guys¹:

The nail which sticks up gets pounded down.

Unlike the squeaky wheel, of course, which gets the grease.

That the former proverb originated in the East and the latter in the West is sometimes held up as an exemplar of the cultural differences.

But, in contradiction to Kipling's famous observation that never the twain shall meet, an indigenous Western expression, courtesy of the Bard himself is:

Discretion is the better part of valor.

But, unlike the nail proverb, this one focuses more on the positive outcomes of keeping mum, rather than the negative consequences.

And one which is indigenous, and focuses on the negative outcomes, but is still offered as friendly advice, not a reprimand, is:

Keep your head down.

And slightly more of a reprimand:

Don't make waves!

or, in a similar nautical theme:

Don't rock the boat!

I suppose it is not so surprising that the West has passed through some bloody and tyrannical ages itself. Apparently when everyone was on boats.

¹ _{"[English] don't just borrow words; on occasion, English has pursued other languages down alleyways to beat them unconscious and rifle their pockets for new vocabulary." -- James Nicoll, rec.arts.sf-lovers, 1990-May-30}