Hi, I was invited by my father to a Buddhism ceremony of putting my grandmother's bone into the headquarter graveyard of the Buddhism sect.
The ceremony is held at the graveyard facility, a property of the temple, and seemingly with reciting Buddhism mantra by monks. The family need to pay to the graveyard to have the monk recite mantra. My family have a family grave, so I think this burial of the bone is done voluntarily with a part of the bone of my grandmother.
I'm sure that my father will feel bad if I don't attend, but it's not dangerous situation for me. My father has a liberal policy.
Is it permissible to attend the ceremony? I guess no.
My rabbi, Rabbi Mordechay Grumach of Chabad Kyoto, recommended me to ask this here, as he feels he is not an expert of Noahide issues and thinks I should be friendly with my family as much as Torah permits.
The link below is the web site of the graveyard, explaining the flow of the ceremony (in Japanese).
https://otani-hombyo.hongwanji.or.jp/main/nokotsu/sodan_nokotsu/
For the information for Noahides in Japan.
The Buddhism faction of my family is Johdo-Shinshu faction.
Burning incense is a common rite in Buddhism ceremony.
This may be for the deceased or to deterrent the bad odor in other Buddhism factions, but in Johdo-Shinshu faction, burning incense is only for honoring the highest-rank Buddha, Amida. (In Buddhism, human beings who found the "truth" become Buddha, an existence transcending the material world. I'm not sure Buddha is a deity, but in Japan, Buddhism was traditionally mixed with a traditional animism, Shinto.) A Johdo-Shinshu altar is commonly equipped with Buddhism statues or tapestry writing "I turn to Amida".
B"H
Shalom Tadamasa!
Here is my opinion:
Under the category of the prohibition of idolatry, there are several commandments on the prohibition of turning to idol worship. On page 145 of The Divine Code (2nd Ed), we read that "if bad feelings, anger, or hatred will arise if one does not attend a wedding that is connected with idol worship, [...] one is allowed to join the celebration even if the others engage in idol worship in honor of the occasion. But each person is individually forbidden to join in any type of celebration or prayer in which the idol is mentioned".
In this ruling, I would replace "wedding" with "funeral", for it the celebration of one's life. Thus, I think you may attend to avoid bad feelings on the rest of your family, but do not join in any idolatrous prayers. If, however, the whole service is focused on idol worship, including consuming food in response to idol worshiping, then I do not recommend you attend.