Hi, Tom!
I installed GP on my other site – samaralife.com – and Google-check-mobile-readiness site says it is not mobile-friendly for two reasons – content width is bigger than the screen and links are too close to each other (since judging by the screenshot menu list isn’t fast enough to transform from the list to the menu as seen on desktops).
Tried with Jetpack mobile theme switched off and on – same results. No other mobile-related plugins installed. Tried deactivating “Move JS to footer” code snippet – same result.