Is it permissible to make Salat and Salam upon the Prophet while the Imam is making the Khutba?

Speech is permissible before and after the khutbah. What about during?

Scholars of the Hanbali school of law discussed this issue in detail. Below is a summary of those discussions.

Speaking while the Imam is praying:
1- As mentioned in the hadith: “Whoever speaks during then he has done something idle, and whoever does idle acts then he has no Jumuah”, this is narrated by Ahmed from Ibn Abbas.

2- Idle speech is not permitted, what then does the madhhab say about useful, purposeful speech?
If the speech is useful but not instigated by the Imam, such as reading Quran, reviewing knowledge, or making Salat upon the Prophet? The stronger opinion is it is not permitted.

3- What if it is in response to something said by the Imam during the Khutba, such as salat due to hearing the name of the Prophet, saying Ameen to a Dua, or similar? This is sunnah to reply to, but should be done silently not loudly.

4- What if it is during the Dua at the end of the Khutbah? The stronger opinion is it is permissible, because the obligations of the khutbah have been met and it is at its end, so one can say Ameen out loud and salat upon the Prophet out loud.

4- What if one cannot hear the Imam, so he busies himself with reading Quran, reviewing knowledge, or making Salat upon the Prophet. The stronger opinion is that it is not allowed.

5- What if a person needs to warn someone of impending danger? Like a blind man who will trip, a child who will get lost, or wealth that is dropped? This is permissible, but should be done with least distrubance possible.

Contemplate the meaning of the hadith mentioned in the beginning and you’ll understand how the Madhhab contextualized the prohibition of speaking and acting by restricting it to idle and frivolous acts, not those with purpose in line with the devotional purposes of Jumuah or the preservation of general welfare.

And Allah knows best

See al-Mubdi, al-Kasshāf, al-Matālib, and al-Rawdh