Shaykh Ṣāliḥ al-Fawzān clarifies that extending or returning the salām during the Friday khutbah is not permitted, whether verbally or by gesture. If someone greets during the khutbah, the salām should be ignored and not responded to, as the khutbah requires full attention.
What is the ruling on extending the salutation [Assalāmu ʿAlaykum] on Friday whilst the Imām is giving the khuṭbah, and is it permissible to return the salām by gesturing with the hand in this situation?
No, none of this is allowed, either extending the salutations nor returning it with the tongue or by gesture. If it is given it should be ignored and not returned.