“There is no such thing as Jewish music that is not influenced by Non Jewish music.”
Arnold Schoenberg’s 12 tone atonal music does not have any obvious influence from any non-Jewish source, although it should be noted that Schoenberg himself claimed that he was following in the tradition of Johannes Brahms, n irreligious non-Jew.
I challenge any chazan to use Schoenberg’s style in tefillah. Schoenberg himself composed a setting of Kol Nidre but it is a tonal work.