我选E,
因为这样的话,这个句子就是很完整的主谓宾结构：
主语：The director's insistence that there be adequate stage lighting and professionally installed backdrops in the theater
谓语：resulted from
宾语：obstinacy和determination to provide a safe work environment for the actors and stage view.
若选B,则变成了主系表结构：
主语：The director's insistence that there be adequate stage lighting and professionally installed backdrops in the theater
谓语：was
表语：obstinate和determined
但这时to provide a safe work environment for the actors and stage view.这串东西就无法归入任何句子成分里了.
而如果看做是被动,即The director's insistence was determined to provide a safe work environment for the actors and stage view.,这样不但逻辑上不通,而且determined 作为动词和前面的obstinate也不平行.