I am used to ground loops between (pro audio) devices being something to be avoided as they're a potential source of noise.
If using (eg) a Nano and a I2C device with multiple Gnd connections as part of a larger circuit, are ground loops anything to worry about.
ie is the Grey wire in this circuit something to be avoided?
Ground loops are always something to be worried about!
Yes.
Put the 4 wires to the breakout board together in one cable. It's not just that the grey wire creates a loop, it's that signals and their associated power and ground wires should travel together in one physical cable or group of wires. Loops of any kind are perfect for picking up all kinds of noise, so if noise is what you want make sure you have lots of loops, otherwise don't.
You have not shown a ground loop. That is merely an additional ground. You only have one load. It takes two loads to make a ground loop.
Please excuse my ignorance.
The two answers above seem to me to contradict each other:
Well, I would say, "yes" to this one. But you need to show your "larger circuit".
They do.
I've seen a lot of answers from @anon57585045 and I know he knows what he is talking about, so I have thought hard about my answer and I still think I'm correct. Maybe I am, maybe not, but I stand by my answer for now. This, of course, does not help you much. Maybe someone else will come along and add something that will clarify things.
This shows that there is no inevitable ground loop between 2 devices.
Multiple devices can be star-connected with the Arduino at the star center, or in a loop (daisy chain...). Such loops should be avoided.
Ground loops in detail are very nasty when caused by multiple power supplies over mains ground (earth) what makes a large noisy loop. Then two devices (one load) are sufficient to build a ground loop.
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