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".