Let's clarify for the unaware masses how people with dual Chinese and American citizenship can retain their dual nationality.

In the past, it was common to enter and exit through Hong Kong, using a Chinese passport (or travel document) when going in and out of mainland China, and using a U.S. passport when entering and leaving Hong Kong. Nowadays, with more visa-free countries, it’s even more convenient.
In the past, those seeking political asylum with more caution would also enter and exit through Hong Kong, and upon arriving in Hong Kong, they would switch to a Chinese passport for entry.
If you're not a particularly important figure, no one really cares about your dual nationality status—don't think too highly of yourself.
Of course, to be honest, when mainland China’s political atmosphere was more relaxed, generally no one paid much attention to these matters. Now, both sides of the Taiwan Strait are applying pressure, and the future is hard to predict. But for ordinary people, there’s no need to be overly anxious.