In 2009, China is Maoist and "Communist" in name only; in fact, much of the awe-inspiring artifacts and sophisticated technologies on display in the parade are principally features of a >= Deng Xiaoping environment - well, maybe starting with Hu Yaoban.
Meanwhile, in 1949 when the authentic Maoists seized power, the US provided entirely nontrivial military aid and financial assistance to the retreating Kuomintang (nationalist) government, and did much to try to suffocate the revolution in its cradle after the PLA did seize power.
Now the US salutes them (and warmly encourages them to maybe continue buying Treasuries... please?), and meanwhile there is nothing in the faintest bit "Communist" about the establishment, save for the nomenclature and iconic imagery of the incumbent power structure.