Once an apolitical confrontation of the world’s best athletes, the Summer Olympics have been increasingly politicized in recent years as the superpowers have denied many of the best athletes’ access to competition.
(A) been increasingly politicized>>> I think it is precise and correct.
(B) been increasing politicization >>> an adverb is needed before the main verb politicized, ohh... have been should be followed by a verb, not a noun, politizication.
(C) been of increasing politicization>>> I couldn't find out why this is wrong, but sounds like it is incorrect. so, excluded it from correct answer.
(D) politicized, increasingly,>>> Summer Olympics cannot politicize themselves, they have to be done by someone or something. been is required.
(E) increased politicization >>> Summer Olympics is an event, not a person. so increase politicization does not go with them.