I think that obviously there are a lot of cultural adaptations which can be made with the Dhamma in terms of external things such as what chants to use and what language they are in, ceremonies, and the details of etiquette, as of course, these things themselves have developed and changed from country to country back in Asia as well.
One thing I think that is worth bearing in mind however, is that this sort of adaptation was more gradual and unguided than how the cultural adaptations have been in the west. For example, I doubt that when Theravada Buddhism was first brought into South East Asia the Monks importing it consciously changed the cultural aspects of it all at once. They probably transplanted the customs along with the doctrine and the things people didn't like faded away.
I think similarly it would be better to try to avoid intentionally cutting out cultural elements, and instead try them out to see if they will be liked. For example, a lot of customs related to chanting and pujas weren't brought into the west very much without even seeing how it would turn out. Perhaps some people would really like the different liturgical chants, either in Pali or in English. Maybe over time new liturgical chants would be written by grouping together passages people like and so forth, and over time, a distinctive western chanting tradition would form that people like and find meaningful. But instead, chanting was in large part cut out of non-monastic western groups.
I for one think it would be interesting to see what would happen if we were to transplant Asian customs and let them develop on their own in a western context instead of cutting them out.
The non-doing of any evil,
The performance of what's skillful,
The cleansing of one's own mind:
This is the Buddhas' teaching.