What is the ruling on greeting those who do not pray, and should one return their greeting?

Question:
I often encounter people in my social life, for example, in the market or at work, who do not pray the midday prayer with us. We have spoken to them more than once, but to no avail. Should I initiate the greeting to them? And if they greet me, should I return it by saying only "And upon you," as is done with Jews and Christians? Please guide us. May Allah reward you with good.

Answer:
If Muslims fall short and display sin, they deserve to be boycotted. They are like disbelievers in that they deserve to be boycotted, even if they greet you. The purpose is discipline; this is a matter of disciplining them and of disapproving of their wrongdoing. If they do not pray, they deserve to be boycotted, and their greeting should not be returned. One should not initiate a greeting to them, nor is one obligated to attend their invitation to a feast if they invite them, nor should one invite them to a feast, until they reform. If it is possible to report their case to an authority that has jurisdiction over them and can compel them to fulfill what Allah has made obligatory upon them, you must do so. This applies whether the authority is a ruler, a committee, a court, or any other body from which it is hoped that the necessary action will be taken in their case. Yes.