I imagine this changes depending on what HT you are using. In my case, it is a Yaesu FT-1XDR, charging in the Yaesu CD-41 charging cradle.
The radio itself doesn't stop me from monitoring a channel when it is in the dock, but I am wondering if it is bad practice to do so.
It's perfectly safe. Note that you will slow charging down, since you are using some of the battery's stored energy to monitor the frequency.
A better solution might be to get a second battery for your radio, along with a charging dock if you don't already have one. With many modern hand-held radios, charging docks increase the charging rate compared to using the charger alone (they must include better charging electronics to permit this). You can put a naked battery into most such chargers, letting you use your other battery on your handheld without being tethered to the charger. As a bonus, having two fully-charged batteries will allow you to go into the field with significantly more runtime capacity with your radio.
Well, it's a commercial product, and I'd be very surprised would Yaesu be willing to deal with the anger if it wasn't safe to do something as obvious as that.
Also, from an engineering point of view, it would be trivial to shut off functionality not safe for use during charging – that literally takes but one transistor.
I'm also not sure what you mean with "not safe"; generally, if you mean "not safe for a human to do", then rest assured that usually, RX operation involves little power and you don't have to worry. What I'd worry about is being close to a transmit antenna's beam when TX'ing at hundreds of Watt.
It should be perfectly safe. I have done it for ages with my Yaesu FT60R handheld so yours shouldn't be any different. Moreover, some people use their handheld as a (semi-) fixed station using a power supply and an external antenna.
The charging cradle is an external power supply that can power the radio and charge the battery at the same time. Yes, that is safe.
