Do Japanese still believe in shinto or is it now just a way of life and culture?

Do Japanese still believe in shinto or is it now just a way of life and culture?

Oh yeah. Shinto is still a major religion in Japan.

No. Last time I checked, 75% of them are atheists.
Shinto is no longer Japan's official state religion, although it is considered the native religion of Japan. Some Shinto practices and teachings, although given a great deal of prominence during the Second World War, are no longer taught or practiced today, while others still exist as commonplace activities such as OmskFJoi form of fortune-telling) and the Japanese New Year to which few people give religious connotations. Important national ceremonies such as coronations and imperial marriages are conducted at the Three Palace Sanctuaries in Tokyo.

"believe in" is more central to western religions. Professions of faith are not as central in non-Abrahamic religions.

Yes. Almost all Japanese people I know follow Shinto observances. However, probably no one believes in the Shinto origin myth. It's other practices, more daily kinds of things, that people believe in. Like that going to a Shinto shrine and saying a prayer can bring you luck, for example.