Is it permissible for a Muslim to claim to be a Christian or of another religion other than Islam for the sake of da‘wah (inviting to Islam), by analogy with the statement of Abraham (peace be upon him), "This is my Lord"?

The path to calling to Allah is through truthfulness and speaking the truth, not through lying and hypocrisy. Allah Almighty says: (O you who have believed, fear Allah and be with those who are truthful) [At-Tawbah/119].

As for Abraham’s (peace be upon him) saying, “This is my Lord,” it was for the purpose of debate to establish proof against his people and invalidate their claims, not as an announcement about himself. He explained that the planets disappear and set, and that the worshipped deity must be one who attends to the interests of His worshippers. Then he moved on to the moon and the sun, showing their weakness, until he said to his people: (Indeed, I am free from what you associate with Allah) after the proof had become clear.

Therefore, it is not permissible for anyone who believes in Allah to claim a religion other than Islam except in a case of compelling duress. How can the interest of da’wah (calling to Islam) be achieved through lying and undermining its foundations? And how can a caller invite people when he has not shown his disavowal from their religion and their shirk (polytheism), when Allah has commanded disavowal from them? (There has already been for you an excellent pattern in Abraham and those with him, when they said to their people, "Indeed, we are disassociated from you and from whatever you worship other than Allah. We have denied you, and there has appeared between us and you animosity and hatred forever until you believe in Allah alone").