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

I recall a Japanese proverb, “犬も歩けば棒に当たる,” of which literal translation is “When a dog rambles around outside, he get a hit with a neighbor’s stick,” meaning, “Don’t come on the surface, don’t try to do anything new, don't say anything, otherwise you’ll be criticized, blamed, or get hurt.”

We have the similar expression, 物言えば唇寒し秋の風　in 和歌 – Japanese classic poem, which can be translated as “In autumn, you feel cold on your lips anytime you utter a word, “ which admonishes you not venture to speak up in public, just be reticent.

It’s understandable that we have a lot of such proverbs and maxims teaching the merit of keeping silent after going through the ages of a tight feudalistic social regime and being severely educated on Confucius doctrines which values silence, and action more than speech, but I wonder if there is the similar saying to “dog and autumn wind” analogies in Anglo-American world where the freedom of speech and the power of eloquence have been highly valued.

I know you have the saying, “Speech is silver but silence is golden” or just "Silence is golden." Are there any other proverbs or set phrases than “Silence is golden.” to admonish you not to speak up, or being self-assertive?

P.S. The focus of my question is "the restraint / gagging of free speech"

Answer

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?