ANSWER:

He can’t be practicing and answering such invitations of shirk at the same time! He must not go there and tell them that his religion prohibits him. 

Sheikh as a Muslim political leader of a state, one has to accept the invitation to attend the other religious programs offering of light,flowers, and water or food for those who believe divine, how he can deal with such situation as fellow Muslim brother’s say he has lost faith in Islam ,even though being a good practicing Muslim.