Do most people in Japan believe in Buddhism or Shinto?

Or majority of them are atheists?

Both. 44% believes in Buddhism, 46% believes in Shinto.

Most Japanese are Buddhist / Shinto, in that order.Many consider themselves both.Each religion can play a different part in the persons life/ death. Like a wedding or funeral.But neither play a major part in the person's life.

Soka Gakkai(Value Creation Society) is the largest lay Buddhist organization in Japan and Soka Gakkai International headquarters for the 12 million members world wide is in Japan. We have have school systems and universities world wide.

http://www.sgi.org/ Soka Gakkai International

Other Buddhist sects don't like us, Proably because The Soka Gakkai
leaders were imprisoned during world war two rather than accepting the Shinto talisman and supporting the militarist government.

http://www.sokaissues.info/home/index.html
Soka Gakkai Controversies Explored

to answer your question I would say that the majority of Japanese are atheists.

they, the majority often participate in the rituals of both religions, but if you ask them if they truly believe the answer most often heard is no.

the majority of Japanese pick and choose their religion to suit the occasion, for example a wedding might be in the christian style, ceremonies to do with age in the Shinto style and funerals in the Buddhist style.

I am thinking about the majority and wish no of fence to Japanese of any faith of which there are many

I agree that most of them are probably atheists or belong to one of the 'new religions' which are mainly offshoots of Buddhism or Shinto, although some are a mishmash of various religions.

I was at a Shinto festival yesterday and asked the priest the name of the deity venerated at the shrine - but he did not know! That just goes to show the depth belief even among the priesthood.

Most believe in/practice a mix of the two, but religion doesn't take over their lives or become a huge deciding factor in things the way it often does with people from the West.

Well actually most Japanese do aspects of both plus. Technically a majority identify themselves as Buddhist but it is very typical for a person over their life to have a Shinto Birth, A Christian wedding and a Buddhist Death ritual.

Most Japanese do not identify themselves as being religious but rather agnostic or atheist.

https://www.cia.gov/library/publications/the-world-factbook/geos/ja.html

http://www.japan-guide.com/topic/0002.html