I agree that Ginsberg, too should recuse herself in those cases.
Recusing herself should be enough. She ought to be able to keep her affiliation if she doesn't rule on any cases involving NOW.
To do otherwise would require, as a fictional example, a justice who is also an Eagle Scout not to attend any Scout functions because the Scouts might have a case before the Court one day.
Yes, she has done more than go duck hunting. She has done it in public, though, which makes a bit of difference.
Also, the Vice President has his own entourage. That makes for much more press coverage.