Getting useful readings out of GSR sensors while moving? I'm currently thinking about a project that would involve using a GSR sensor and an Arduino (Probably the Grove GSR Sensor) to measure Stress levels in a person. 

It will not be a research project, but an art project instead. I want to build a device that shows my stress level with some LEDs as indicators. The idea is that I can walk around with it and when I approach people and talk to them the color changes because of my social anxieties. So it doesn't have to be accurate, but if it won't work at all, I might as well scrap the project.

In which ways would movement of the subject distort the readings? Suppose the wearer has heightened physical activity, would the GSR sensor give any useful readings? And if so: any pointers on how to pull this off?
I think the general downside of the galvanic skin response (GSR) apply here. Wikipedia sums up a few confounding factors that affect the validity of GSR: 


Temperature and humidity (affect the resistance of the skin and hence GSR);
Internal factors, such as medications and hydration;
Different locations of measurement on the body can lead to different responses; for example, the responses on the left and right wrists are driven by different regions of the brain, providing multiple sources of arousal. 
Different body parts may have different sweat gland density 
Electrodermal responses are delayed 1–3 seconds.


My personal biggest issue with the method is the fact that the GSR depends so much on the temperature of the room and activity of the subject. However, my purpose for it is a quantitative one; your is more of a qualitative one as I understand it. If yes, then some variability may not be so problematic and you can counter the above drawbacks by 


Only do the experiment indoors in a climate controlled environment;
Calibrate the equipment on yourself and only use yourself as a subject and stay hydrated;
Always use the same location (fingers in case of your linked device);
Give your device some time to respond; so the (stress) situation has to be somewhat prolonged, and the response will be delayed.  


Do note that skin conductances are finicky. You can assure good contact by rubbing the skin with alcohol and a rough-surface pice of gauze. Make sure to apply some conductive paste. Measure the impedances regularly.  

FYI: I have chosen to use pupillometry as a measure of stress. It has its own drawbacks and issues (especially adaptational responses and baseline issues), but once it works, it's less prone to signal drift, e.g. because of impedance issues as with electrode-based methods.

Below I've added a reference that lists an entire protocol for such measurements.

Reference
- Cartocci et al., J Vis Exp (2017); 126: 55872