There are a couple of key goals involved with infiltration. One is to corrupt within, sowing confusion, creating social and moral chaos to cause Western civilization to implode, leaving a power vacuum and moral void to be filled by Communism (or whatever other ideology is intended). Another is to use the institutions and power of the Church to advance direct Communist goals. And, of course, it's just a very large labyrinthine bureaucracy for people who are up to no good to hide. Prior to, say, the 1960s, the hierarchical structure of the Church could be used in an authoritarian or dictatorial sort of way. A Communist infiltrator who attained a certain level of authority good give orders to people without question. Money could be hidden, stolen, and manipulated. Religious houses could be used to hide agents and so forth. It's a logical strategy. In fact, American and British intelligence agencies have not overlooked religious institutions as covers for various covert operations. One could certainly suspect that some aspects of the leftward turn in Church affairs was not just because intellectual clergymen had been convinced by the "brilliant" ideological arguments of socialism and liberalism. [irony alert]