Karate is Okinawan in origin, developing from a mixing of Okinawan Te and Chinese Quanfa. Some styles, like Uechi Ryu, are more heavily Chinese influenced. By the 1930s there were also Japanese influences making their way into karate training.
The dojo concept and design also tends to be Japanese. From the various writings about karate schools 100+ years ago, tradition would appear to have been training in the teacher's back yard. Pretty common in China too it seems.
We utilize a uniform and belt-ranking system borrowed from Japanese judo. Check out George's books (among others) for pictures of what students in Okinawa wore while training before the dogi was adopted...think of how your students would react to you trying to enforce that tradition!

As was mentioned above, the clapping and bowing ritual (not to mention seiza) come from Japan and Shintoism. Historically Okinawa has been more influenced by Taoism and Confucianism, and to a lesser extent Buddhism, but not as much by Shintoism. Most of the educated karate practitioners in the 1800s were schooled in the writings of Lao Tsu and Confucius. The Shinto influence coincided with the increased control of Okinawa by Japan starting in the late 1800s.
Not exactly a lot of pictures on Okinawa a century or so ago either, although I believe it was common on Okinawa for most households to have family shrines to honor deceased family members. My understanding is that if a student wanted the spirits of deceased teachers to watch you, you went to their tombs, paid your respects, and demonstrated your skills there, most often privately.
The dojo and dogi, while starting to make appearances in the 1920s and 1930s, really seem to have taken off post-WWII when karate became a Japanese phenomenon. I think it fair to say that the traditions we currently have for a shomen with pictures, as well as clapping and bowing to those pictures, appeared at the same time.
So in 2005, the "traditional" Uechi Ryu practioners train in a Chinese style modified by Okinawan and Japanese training influences, in a Japanese-style room/building, while wearing Japanese-style uniforms, and practicing Japanese rituals.
So again, what is traditional for a karate school and by whose standards? And if karate can be so heavily modified by Japanese culture when the Japanese adopted it, why can it not be modified by American culture when taught here?