No, a non-finite clause as well as a finite clause can be a supplementary clause (which is what you call 'a non-defining clause'). And if you're to use a finite clause there, it should be not which is but which was, because the supplementary clause is about the late nineteenth and early twentieth centuries.
The most widely accepted theory, which was championed by anthropologists in the late nineteenth and early twentieth centuries, envisions theater as emerging out of myth and ritual.
Here are some of the many, many examples found in news articles and books:
Tyndall believed it was vital for improving human health that the germ theory, championed by people like Louis Pasteur and Joseph Lister, be shown to be true.
(From this Guardian article)
The other dominant theory, championed by anthropologist Donald Symons in his 1979 book The Evolution of Human Sexuality, holds that the female orgasm, like male nipples, evolved as a byproduct of natural selection.
(From this Quartz article)
The second major theory of our times is transformational leadership theory, championed by James McGregor Burns (2003), as well as by Bernard Bass and Bruce Avolio (1993).
(From the book What’s Wrong With Leadership?)