1) Buddhism is not a religion by the Western definition of a religion. Prince Siddhartha invented it in Hindu India as an attempt to alleviate his subjects' suffering. The prince was a sensitive sort, raised on philosophy and given to long bouts of introspection, and he assumed the poor commonfolk were just like him. He thought that while they labored in the fields and struggled to find enough to eat, they'd find spiritual peace in navel-gazing. Somehow, it caught on.
2) As with any ancient tradition, there are many approaches. Zen is actually the Japanese version of Buddhism, imported through China. In China it's called 'Chen'.
3) In the United States, we think it's more romantic to go back to Buddhism's Indian roots and add some Sanskrit. Or even better, we add a sprinkle of Tibet. Yes, even if we're practicing a strain of Buddhism that came through China and Japan.
4) Some people try Buddhism after quitting their previous religion, which gives the impression that Buddhism is equivalent to Judaism or Christianity or whatever. However, you don't have to quit anything, just like you don't have to cancel your AAA membership to join a knitting club. Zen Buddhism offers additional spiritual services, but it doesn't replace any spiritual commitments you've already got.
5) Zen Buddhism is the strain of Buddhism that focuses on koans and nonsense. If you don't find nonsense enlightening, Zen is probably not for you. It has nothing to teach. Its purpose is to put you in a state of mind where you can realize the futility of pain and worry, and thusly be liberated from yourself.
6) This approach is heavily based in Hindu philosophy. Study up on Hinduism if you're totally lost.
7) Zen is not a replacement for talk therapy. If you expect other people to actively help you resolve your problems, Zen will be nothing short of infuriating. Zen is only useful if you plan to resolve your problems by yourself anyway, and you just need the right state of mind to do it. If you're studying under a Zen master, the Zen master doesn't actively guide you; he/she just gives you koans.
8) If you know what to do with koans, Zen is a lot of fun.
9) Zen Buddhists do have temples. Practicing Zen Buddhism in Buddhist temples is illegal in Communist China. However, maintaining the temples and their traditions for 'historical purposes' is sanctioned by the state.
10) Hey, it's not the kindest, gentlest government policy, but it used to be worse!
11) Not-religions are fairly common in China. Confucianism is another not-religion. It teaches loyalty to the family and offers a code of conduct for economy and trade, as well as diplomatic relationships between government bodies. Confucianism is essentially the study of one man's insight into traditional Chinese culture. A lot of the traditional values (pre-Communism) are reflected in Confucianism.
12) Maoist Communism offers many competing, contradicting philosophies. The Chinese people have had to get used to balancing all these philosophies. And the philosophies keep coming - nowadays there's something that could be called Post-Maoist Communist philosophy, which embraces capitalism (sort of). All these rapidly changing philosophies go a long way toward explaining the Chinese people's attitudes in life!
It's gotta be hard. You never know what to expect a day, a week, a year from now. Good thing they haven't completely forgotten their Zen. Prince Siddhartha would be sympathetic.