This practice is not limited to any place or time ... we drop all thought of place and time. It certainly is not Indian, Chinese, Japanese, French or American. But, of course, we live in place and time, so as Buddhism traveled over the centuries from India to China, Japan, Korea and other places, it naturally became very Indian/Chinese/Japanese/Korean etc.
But what of the cultural trappings?
Must we bow, ring bells, chant (in Japanese, no less), wear traditional robes, have Buddha Statues, burn incense? ... All that stuff besides Zazen. Are they necessary to our Practice?
No, not at all!
We don't need anything other than Zazen, any of those trappings. In fact, they are no big deal, of no importance, when we drop all viewpoints in sitting Zazen.
On the other hand, we have to do something, to greet each other somehow, read some words, dress some way. Why not do such things? As I often say, for example, we have to do something with our hands when practicing walking Zazen ... why not hold them in
Shashu (I mean, better than sticking 'em in your pockets)?
As well, there are parts of our practice which we do
BECAUSE we resist (for example, when visiting a temple for Retreat, I usually put my heart fully into ceremonies and arcane rituals BECAUSE I resist and think some of it silly or old fashioned). Ask yourself where that kind of resistance is to be found (here's a clue, and it is right behind your own eyes).
What is more, there is method to the madness, and many (not all) customs have centuries of time tested benefits ... embody subtle perspectives ... that support and nurture Zazen Practice at the core. Many parts of our Practice, though "exotic", are worth keeping, even if they strike someone as strange at first. Bowing, statues, rigid decorum in the Zen Hall and, yes, weird talks about Koans and arcane ceremonies all fit in that category. They may seem like unnecessary "Japanese" or "Esoteric" elements at first, until you understand the role they serve. I have given talks on all these things recently, for example ... the humility and wholeness of Bowing.
Many aspects of tradition can be
seen in new ways when the barriers of the mind are knocked down. Thus, for example, the Kesa, the Buddha's Robes ... though just cloth ... can be seen to cover and enfold the whole universe, laughter, cries of pain, old age, becoming and fading away ... life ...
On the other hand again, it is okay to abandon or reject many practices. However, KNOW very well what you are rejecting before you reject it.
Absorb what is useful and discard the rest. For example, I think Oryoki [formal meal ritual] is a great practice, and worth keeping.. Same for bowing.
When tasted as such ... every action and gesture in this life is Sacred and Magical when experienced as such, from changing a babies diaper to cooking dinner to chanting the Heart Sutra. So, why not Chant as well as the rest?
Some things I keep
out of respect for TRADITION [the robes, the ways of doing some ceremonies]. It is important to keep ties to where we come from. Some things also have a special symbolic meaning if you look into them, so worth keeping [for example, a Rakusu]
But other stuff, no need to keep: For example, I usually avoid to chant in Japanese or Chinese [except once in awhile, out of respect for tradition]. Tatami mats and Paper screens have nothing to do with Zen practice particularly [but I happen to live in an old Japanese building, so ... well, tatami and paper screens!}

Some things I think are just dumb (except symbolically), like the Kyosaku stick. Incense is great, until it was recently shown to cause cancer. Many beliefs of Buddhism are rather superstitious things that were picked up here and there. I abandon many of those.