Does the prophetic hadith, "And whoever touches pebbles has babbled," prohibit only the one who causes disturbance, or does it also include the one who tries to silence him?

“Whoever touches pebbles has babbled,” because by moving them, one distracts oneself and others from the sermon, and “If you say to your companion on Friday, ‘Be silent,’ while the Imam is delivering the sermon, you have babbled.”

The prohibition here is against speech, not against gesturing. Therefore, it is permissible to gesture to alert someone who is speaking. The Companions gestured to those who spoke in the presence of the Prophet (peace be upon him) to be silent. Gesturing is permissible in prayer, so it is even more permissible during the sermon.

Ibn 'Umar's throwing of pebbles does not fall under the prohibition, because it was for alerting. His action might have been due to the man not being close or directly in front of him. However, it is contrary to what is preferable, and it was not the common practice of the people, because glorifying God (tasbih) and gesturing are better.