I have several iPod Shuffles (2nd Generation). They all work with my old MacBook (running 10.6.8 and iTunes 11.4). But a newly acquired 2GB one will:
Connect and work with MacBook (OS 10.6.8 + iTunes 11.4)
Connect and be recognized as an iPod by Lenovo p50 (iTunes 220.127.116.11 for Windows)
Will not be recognized by MacBook Pro (OS10.14.6 + iTunes 18.104.22.168)
Or more specifically, it's not recognized by iTunes on the MacBook Pro. In Apple menu > System information > System report > Hardware > USB > USB 3.0 it shows up as an iPod device when connected, but never shows up within iTunes, either when it already has something on it, or when it's been freshly restored, either with the iTunes from the MacBook or the Lenovo.
I have restored it several times, I have used four different 2nd Gen connector docks, I have connected a different 2GB iPod Shuffle 2nd Gen to the MacBook Pro and that different one works fine.