Greenpeace is not against purse-seining, which may surprise some people. Sure it's a big industrial-looking fishing operation, involving huge nets and catching lots of fish. But that's not always a bad thing.
If we are to assume we're still going to catch and eat fish, then purse-seining as a method is probably going to be something that continues. Purse-seining involves setting a large circular wall of net around fish, then 'pursing' the bottom together to capture them. Where purse-seining is best used is with large single-species schools of fish, that shoal tightly together. Examples like herring or mackerel spring to mind. These can be caught relatively 'cleanly' by purse-seining.