I'd say it's quite safe. When you start your car, there is a huge drop in battery power, not surge (remember how your lights dim the moment you start). Now, the undervoltage is not good for electronics either, but typical gadgets have 5V input and use an adapter (a buck converter actually) to transform 12V to 5V. Such converters are usually rated for a wide input voltage range (something up to 15V) and require about 2V for themselves to work correctly, so as long as the battery voltage doesn't drop below 7V or so, your gadgets don't even see any change on their power line.
For a second line of defence, most gadgets have an internal battery to fall back on, should the input voltage become unusable.
As a personal experience, I have been using a GPS plugged into my cigarette lighter for 3 years now. I also use a dashcam, which I unplug only when I need to charge the bluetooth handsfree or several of my mobile phones. None of these devices have had any power-related issues. If anything, I can suggest you don't unplug the gadgets unnecessarily, since the only issue I've had is my GPS power cable broke down because of repetitive unplugging (I prefer to remove the GPS from the car when I leave it on the streets overnight). Not that it proves anything, but I suppose it stands as confirmation for the things said above.