It’s not entirely clear, but it appears to be up to the instance operator.
Users can disable referer headers in their browser settings which overrides anything the instance operators can do.
Only nerds do stuff like mess with their browser settings through about:config. The bulk of activity is from people who don’t mess with those settings and don’t stay aware of what’s going on. Those are the ones who the info gatherers want to observe, so that’s why the system should be opt-in in every case, and it’s also why they want it to be the opposite.
There’s legitimate interest in knowing where people come from, though, and asking on your own page “how did you get here?” is hardly going to work. Personally I don’t think it’s much of an issue if some random commercial site sees that I got there via lemm.ee, it’s not giving away much at all, not even whether I have an account here and certainly not as much as tracking cookies. OTOH I also think it could be done better, wich tech similar to Mozilla’s aggregate (i.e. you’re just a number in an anonymous mass) ad clickthrough thing. Sites would see “yep we got a number of visitors from lemm.ee, and that number from lemmy.world” but wouldn’t know which of their site impressions corresponded to which origin.
If people dont care enough to mess with their browser settings thenselves, then they can either a. join a privacy-focused Mastodon instance whose admin will keep the “no referer” policy, or b. live with the fact that choices are being made for them. People need to take actions for themselves, we cant treat everyone like babies.