I've been there many times, behave yourself reasonably and there's no issue. It's nothing like it was like behind the Iron Curtain. We've been there upwards of 20 times by now, we have to show passports for trains, hotels and to register our stay (most of the time we are with relatives rather than in a hotel which means we have to register with the police. Normally the hotel takes care of this for you.)
In all that travel we have had two quasi-encounters with the police--in both cases we were passengers in cars stopped for non-driving issues. (The first time the driver looked Japanese and I'm obviously not Chinese--and you pretty much can't drive on a foreign license over there. The second time the car was actually lacking a required permit, the driver got a ticket for that.) Neither time did they care one bit about me. (My wife is China-born, they wouldn't realize she isn't a local.)