Why do some people enter the mosque and pray “Tahiyat Al-Masjid” (two rak'ahs upon entering the mosque) during the Friday sermon, even though the Imam says: “Whoever babbles, there is no Friday [reward] for him, so be silent”?

It is obligatory to listen to the Friday sermon and not be preoccupied from it with anything, even if it is enjoining good or forbidding evil. An exception to this is greeting the mosque (Tahiyyat al-Masjid) because the Prophet, peace and blessings be upon him, commanded it for whoever enters the mosque during the sermon.