Praise be to Allah, and peace and blessings be upon the Messenger of Allah, his family, and his Companions. To proceed:
The basic principle is that Islam calls for justice and good conduct toward all people, while at the same time preserving the belief in the Oneness of Allah (Tawhid) and avoiding the affirmation of any false or polytheistic meaning.
When some Christians say, “The peace of Christ,” they may simply intend it as a customary greeting, while at other times they may intend a religious meaning connected to their beliefs about Christ (Jesus, peace be upon him).
Therefore, it is safer for a Muslim not to respond with the same phrase if it contains a religious meaning that contradicts Islamic belief, because true peace comes from Allah Almighty alone, and He is:
“As-Salam (The Source of Peace).”
As for Jesus (peace be upon him), he is a servant and Messenger of Allah. We believe in him and love him, but we do not attribute to him any of the characteristics that belong exclusively to Allah Almighty.
Therefore, if someone says:
“The peace of Christ.”
You do not have to respond with the same phrase. Rather, you may use clear and sound expressions such as:
“And peace be upon you.”
Or “Peace be upon you.”
Or “Peace is from Allah.”
Alternatively, you may simply give a polite response that does not imply approval of any false religious meaning.
If the person intends to provoke you or to express a polytheistic belief, a Muslim should not participate in that or affirm such a belief.
At the same time, the response should be given with wisdom and calmness, without injustice, insult, or aggression. Islam combines steadfastness in faith with good conduct toward others.
Conclusion
It is not permissible to affirm polytheistic meanings or expressions based on false beliefs.
It is preferable not to repeat the phrase “The peace of Christ” in the same wording if a religious meaning contrary to Islam is intended.
One may respond with correct and general expressions such as “And peace be upon you.”
If it is intended merely as an ordinary greeting, the matter should be handled with wisdom and gentleness.
If the intention is provocation or the expression of a false belief, the Muslim should neither approve of it nor repeat it.
And Allah knows best.