I ought to note that this isn't a trend merely among Marxists. The name of the country of Qatar, long pronounced 'ka-TAR', (and this is the pronunciation in my dictionary) became nearly universally 'cutter' in the broadcast media, following Condoleezza Rice. So what if that is the way locals say the name? We say it otherwise. Should we insist that the French say "United States" instead of États Unis? Should we call Germany Deutschland? Such is the power of the mass media. But certainly, when traveling to foreign lands and using the local language, one ought to use the local pronunciation, for that is the polite thing to do.
The name of the Chinese city means, both now and then, "Northern Capital". What did change was the system used for converting Chinese ideograms into roman letters, replacing systems developed by Europeans with the homegrown Pinyin system. This system varies greatly in places from Latinate pronunciation: for example, 'd' in the Pinyin system is pronounced 't'.
Under the new system of spelling, the word Beijing is pronounced, roughly, 'Peking'. The Chinese themselves didn't rename their capital. So nothing really changed, and the joke is on us. Perhaps the Chinese are irritated that Westerners started using a new name for their city.