A signaling ground loop isn't going to be a problem for Ethernet.
A power ground loop could be a huge problem. This doesn't have anything to do with signal quality, but suppose your shed was fed without grounding (e.g. a pre-1966 regular circuit, a pre-1996 dryer circuit, or a pre-2008 subpanel). You have a ground fault or a bad connection on the neutral wire. What happens?
On a pre-2008 subpanel: Normal 120V return current wants to get back to source (the transformer neutral). The neutral wire does that normally, but suppose it has a bad connection. These obsolete installations combined neutral and ground, but it's broken. So neutral current will seek through all ground connections back to the main panel or supply transformer. One of those ground connections is the foil wrapper on your shielded ethernet - it's suddenly carrying 11 amps of neutral current. So it's glowing cherry red. Not good!
On a grounded power strip fed off an ungrounded 120V line: All the system grounds are together, but not connected back to the main panel. So the PC power supply has a hot-ground fault. If proper grounding was present, that would flow 77 amps on the ground wire and trip the 20A breaker. However, it's not. But, it is connected to the ground on the router, which is connected to the foil wrapper on the Ethernet cable. That foil has high resistance and will only flow 18 amps, so the breaker does not trip, but the foil sits there glowing cherry red. Not good!
So your problem is utility ground current traveling on that shielded Ethernet shield, and the solution is make sure the supply wiring to the shed has grounding that is absolutely tip-top. If the grounding is good, current will flow all paths in proportion to their conductance (1/resistance), but the proper ground path will be very high conductance so the ethernet's share will be minimal.
By "grounding" I mean ground wires back to the panel. Code may also require ground rods for non-attached buildings, but those are for lightning and ESD, and can't really carry 12 amps @ 120V. If it could, we wouldn't bother to mine copper.