His Christian family start the meal with a supplication to Jesus; what should he do?
We praise Allah for having guided you to Islam and we ask Him, may He be glorified, to bless the rest of your family with that. And we advise you to treat them kindly and be gentle in calling them, and strive hard to guide them, for that is the greatest thing you can give to them.
Asking Jesus (peace be upon him) to bless the food is a kind of major shirk (associating others with Allah), because it is calling upon someone other than Allah, may He be exalted. So it is not permissible to join in with it or to keep quiet about it when it is possible to object to it. If a person is unable to object to it verbally, he should object to it in his heart and leave the place, because Allah says (interpretation of the meaning):
“And it has already been revealed to you in the Book (this Qur’aan) that when you hear the Verses of Allaah being denied and mocked at, then sit not with them, until they engage in a talk other than that; (but if you stayed with them) certainly in that case you would be like them. Surely, Allaah will collect the hypocrites and disbelievers all together in Hell”
Al-Jassaas said in Ahkaam al-Qur’aan (2/407): In this verse there is evidence which indicates that it is obligatory to denounce evil to the one who is doing it. Denouncing it includes expressing dislike, if it is not possible to remove it, and leaving the place where the one who is doing it is, and staying away from him, until he stops doing it and does something else. End quote.
Based on that, what you have to do is either object to their prayer or get up and leave when they start to do that. Perhaps it is better to come a little bit late, after they have started the meal, so that you will not hear their prayer.
If the family will listen to you and accept your call, then it is better for you to explain the reason why you left or why you come late, and tell them that Islam places great emphasis on enjoining what is good and forbidding what is evil, and that Islam does not approve of calling upon anyone other than Allah, and it does not approve of its followers listening to wrong words and approving of them.
We ask Allah, may He be exalted, to increase you in knowledge and guidance.
And Allah knows best.