The China of the present day is not anti-religious. All the government wants is a degree of control over all religions operating within its territory (due to China's bad historical experience with cults evolving into rebellions). Yes yes I know it's paranoia...
The whole hoohah could have been avoided if there had been dialogue between the two parties, and thus suitable candidates acceptable to both could have been chosen. The Vatican however, is a political as well as a religious entity, and currently still recognizes the ROC in lieu of the PRC which is, of course, unacceptable to China. Thus no direct communication, thus we're back to square one.
The result is the Vatican appoints its own bishops who can't operate in China, and China appoints its own bishops who end up getting excommunicated.

Rest assured, though, that Catholics here still get to pray in church, hear Mass and everything. They're just cut off from the outside world, that's all.