In 1988, the Council on Economic Priorities began publishing Shopping for a Better World,
with the simple thesis of consumers having the power to change companies by the simple expedient of refusing to buy.
Option Elimination -
(A) with the simple thesis of consumers having - "with" introduces a prepositional phrase that can be adverbial or adjectival depending on the context. But the real issue here is "having." Let me share the proper usage of "having," and then let's evaluate this option. Having finished his work, John went for a walk." But we don't see any such usage here. Moreover, "thesis of consumers." Really? Wrong.
(B) which had the simple thesis of consumers having - the same issue of "having."
(C) where the thesis was simple: consumers having - "where" is a location marker. Wrong. Moreover, it is still the same issue of "having."
(D) with a thesis that is a simple one: consumers have - what is "one" as a pronoun referring to? Thesis? Are we saying "thesis that (that refers back to thesis) is a simple one (refers to thesis) so it looks like "with a thesis thesis is a simple thesis" Really? Atrociously wrong.
(E) whose thesis was simple: consumers have - "whose" can refer to people or things. Here, it clearly refers to "Shopping for a Better World" is some publication. Ok