This is another huge and very complex issue. It is also a very emotional issue, because it often leads to the question of loyalty to the family, which is the cornerstone of Japanese culture. There are not always clear cut answers to many of the questions, and so it's important to help students understand some of the Biblical principles that should guide them. Beyond that I feel that we need to leave it between the individual and God to do what is and isn't appropriate. It's important to remember that different families attach different significance to different customs.
Some Japanese families are strongly Buddhist.
But by far the majority are Buddhist or Shinto in name only. The mark of a Christian is love, which means we care deeply about people and what is best for them. Be consistent in what you will do and what you will not do. People will come to respect your convictions. Always remember, God is at work, and will use your faithful witness for His glory.