Self-censor

Children haven't learned how to self-censor, and are likely to say very inappropriate things at very inappropriate times.

Source: tatoeba (3786262)

We all self-censor, often without even realising it, that is, we tailor our words and actions to suit the occasion.

Source: tatoeba (3786286)

The harassment can lead journalists to self-censor, remove themselves from online platforms, sometimes permanently, or even lead to women quitting journalism altogether.

Source: tatoeba (12236044)

There's been a lot of talk recently about the problem of "libel chill" on British science writing, that people self-censor for fear they'd be sued (as Simon Singh was by British Chiropractic Association).

Source: wiktionary