In fact, a Muslim is encouraged by the Sunnah to repeat the words of Adhan (Call to Prayer) after the muezzin. Sheikh M. S. Al-Munajjid, a prominent Saudi Muslim lecturer and author, states:
“Al-Hakim reported in Al-Mustadrak (4/359) that Anas ibn Malik (may Allah be pleased with him) quotes the Messenger of Allah, peace and blessings be upon him, as saying: ‘There will come a time when people will sit in circles in the mosques and they will have no concern except this world. Allah has no need of them so do not sit with them.’” This is a Sahih Hadith even though Al-Bukhari and Muslim did not narrate it. Al-Dhahabi said in Al-Talkhis that it is Sahih.”
This Hadith states that this blameworthy deed is disliked, because the mosques are not built for such a purpose. Allah commanded that mosques should be built to remember Him and to conduct Prayers and acts of worship and obedience to Him, such as I`tikaf (retreat, seclusion for devotion and worship), and different kinds of Dhikr such as circles for reciting Qur’an and seeking knowledge.
On the other hand, there are Hadiths that command us to repeat the words of the Adhan after the muezzin, as a Mustahabb or encouraged deed.
Some people neglect this fact, and do not realize how much reward they are missing out on and how much they are to blame for that. What sort of hearts must they have?! They hear the remembrance of Allah, then they turn away from Him, and it has no effect on their hearts so that they may fear Him and feel compelled to listen.
One of these Hadiths is that narrated by Imam Muslim in his Sahih (No. 384) from `Amr ibn Al-`As (may Allah be pleased with him), who said that he heard the Prophet, peace and blessings be upon him, say: “When any one of you hears the muezz
in, let him say the like of what he says, then send blessings on me, for whoever sends blessings on me, Allah will send blessings tenfold on him. Then ask Allah to grant me Al-Wasilah, for it is a status in Paradise that only one of Allah’s slaves will attain, and I hope that I will be this one. Whoever asks for Al-Wasilah for me, will be granted my intercession for him.”
As for greeting each other with Salam and shaking hands, there is nothing wrong with this, for these are acts of obedience to Allah. There is no conflict between doing these things and responding to the muezzin, because a person may do all of these things at once.
Moreover, Muslims should beware of doing anything that may offend or disturb those who come to the mosque for worship. This includes disturbing those who are reading Qur’an, praying or remembering Allah in the mosque. It is an evil deed to disturb the people in the mosque by talking about worldly affairs, because this is offensive to them and distracts Muslims from doing acts of worship properly. Ahmad ibn Shu`ayb Al-Nisa’i reported in As-Sunan Al-Kubra (5/32) a report from Abu Hazim Al-Timar from Al-Bayadi, that the Prophet, peace and blessings be upon him, came out and found the people praying and reciting in loud voices. He said: “The one who is praying is conversing with his Lord, so let him think about what he is saying to Him. Do not compete with one another in reciting Qur’an loudly.”
Ibn Muhayrez (may Allah have mercy on him) is reported to have said: “Speaking in the mosque is idle talk, except for one who is praying, or remembering his Lord, or asking for help or giving help.” (Musannaf `Abd Al-Razzaq, part 8).
Ibn Al-Haj said, concerning the etiquette of the Muslim when setting out for the mosque: “He should intend to avoid idle talk in the mosque or talking about that which does not concern him, for there is a report that says that speaking in the mosque about anything but the deeds of the Hereafter is like fire in dry wood, it eats up rewards (of good deeds). So he should take care to avoid this…” (Al-Madkhal by Ibn Al-Haj, part 1).”