Rav Moshe Feinstein dealt with this question in terms of calling for silence before shofar blowing, and I have translated the bulk of his responsum (Igrot Moshe Orach Chaim 2:36) below. I particularly like his last suggestion here – that there is a third choice, separately notifying those who will listen. This requires more work, of course, but that's an important point: Often a rabbi can do better for his community by putting in the extra work.
Herewith the translation:
Regarding the matter of whether to announce before shofar blowing that one may not interrupt verbally until after the "standing blasts" [the second set of 30 blasts, blown during Musaf], in a shul where many simple people daven and it is known that they will not listen to the announcement, and they will interrupt. One person contends it would be better not to announce this, so that the people would sin accidentally rather than intentionally. His honor [the letter-writer] responds: Should we fail to teach the general population any laws because of such a concern, saying regarding them, 'Better that they sin accidentally'?
The principle of 'better that they sin accidentally' applies specifically where people definitely will not accept, as seen in Tosafot Bava Batra 60 and Rosh to Beitzah 30. We should not teach such people. The question of how we could refrain from teaching is not difficult; since they definitely would not adhere even were they to learn it, there would be no benefit in teaching them.
However: If it is unclear that they will not accept the law, we definitely are obligated to protest their conduct, and all the more so to teach them outside of the time when this violation is occurring.
It also appears obvious that when someone comes to learn, we definitely teach him everything according to the law, even if it is clear that he will not accept it. One should not teach incorrectly just because the listener will not practice it. It is only when they do not ask, that we do not independently protest. But in this case [where they ask], there is no issue of 'better accidental than intentional.'
It also appears obvious that if the population includes people who will listen, one must inform them of the prohibition – even if it is known that some will not listen and will violate intentionally. We do not harm those who would accept the instruction in order to avoid harming those who will violate the law intentionally and be punished as intentional sinners. Were we not to inform these people, they would violate accidentally, which would also be a legal violation, causing harm.
Therefore: In a shul which may include people who do not know the prohibition against interruption, and who will interrupt [the shofar blowing] and accidentally break the law, but who would listen if it were announced and would not interrupt, we must announce the law unless there is a way to convey the information to those people individually. If it is known that no one is present who will accept it, or if there is some way to inform only those who might listen, then we should not announce it.
Note: For lack of time I didn't translate his last paragraph, which includes a separate, fascinating point on the problem inherent in teaching a chumra as though it were law. Here it is:
וקצת יש להסתפק בדין זה דאסור להפסיק גם אחר תקיעות דמיושב עד שיגמור תקיעות דמעומד שלא ברור האיסור דהר"ן בשם בעה"מ סוף ר"ה הקשה ע"ז דמידי דהוה אמדבר באמצע הסעודה והובא בט"ז סימן תקצ"ב סק"ב והתירוצים דחוקים והר"ן מסיק דרק משום דהביא זה הרי"ף בשם הריש מתיבתא צריך ליזהר בזה עיי"ש, ונמצא שאף אם במזיד יפסיק בדבור לא יעבור באיסור ממש אפשר ליכא בזה משום מוטב שיהיו שוגגים וצריך להכריז. או אדרבה כשיכריזו שאסור ויעבור יהיה עובר יותר מצד מחשבתו שהוא יסבור שהוא איסור ממש, שיש ע"ז עונש אף שבעצם אינו איסור ממש כדדריש ר"ע בקידושין דף פ"א וכשלא יכריזו הרי יהיה רק שוגג בדבר שהוא רק חומרא בעלמא שאולי לא יענש ע"ז ואין להכריז, ואין בידי לע"ע הכרעה בספק זה. ולכן יש לעשות כדלעיל שאם אפשר שיקבלו איזה מהשומעין צריך להכריז שאסור להפסיק ואם ידוע שכל האין יודעין הדין לא יקבלו אין להכריז. ידידו מברכו בחג שמח, משה פיינשטיין.
