This is not a very important factor. If someone can be a Christian by following 99% of the tenets, the same can be said of Communism. Communism is mainly an economic system with atheism thrown in.
Your point on China is invalid. In general, most Asians do not care for Communism and it has been foisted on them. In case of Europe and Latin America, the people have a natural attraction for Communism.
Catholic church is very much socialist in character and Communism is very close to socialism. So it is both the church and the people. The only reason America is not like Europe is that the American Constitutional Republic was set up by Protestants. If Catholics had dominated the adoption of the Constitution, they would have made it a socialist system.
-—Catholic church is very much socialist in character and Communism is very close to socialism-—
Some papal encyclicals:
On Socialism
http://www.ewtn.com/library/ENCYC/L13APOST.HTM
At the very beginning of Our pontificate, as the nature of Our apostolic office demanded, we hastened to point out in an encyclical letter addressed to you, venerable brethren, the deadly plague that is creeping into the very fibers of human society and leading it on to the verge of destruction...
On Atheistic Communism
http://www.vatican.va/holy_father/pius_xi/encyclicals/documents/hf_p-xi_enc_19031937_divini-redemptoris_en.html
On the Doctrines of the Modernists
http://www.vatican.va/holy_father/pius_x/encyclicals/documents/hf_p-x_enc_19070908_pascendi-dominici-gregis_en.html
Can someone be a Muslim by following less than 100% of the tenets?