""In sampling for plankton in the Antarctic from Tara, every sample had degraded fishing net fiber in it.""

A likely source would not be "gill nets" that some refer to here.
A few countries actively fish in the antarctic using mobile trawls. I suspect regulations and enforcement is relatively low, if active at all. The krill fishery uses very fine mesh trawls. (Some folks question the wisdom of catching forage fish so near to the bottom of the food chain in such an environment).

Can one rule out an additional source, scientific research?