Every group has their core segment that is in an adversarial relationship with other group segments and with everyone else outside the group, AKA the unworthy non-entities. Elitist, racist, bigoted, nationalist.....it is all the same pack animal hatred/fear of those outside the group, and of those not deemed worthy to join. Not allowed to practice Judaism because of lacking a genetic connection is a humbug.
Gwyneth Paltrow and her children aren't Jewish, segment or otherwise. They are no more a segment of Judaism than they are a segment of Mormonism.
If she wants to convert she can do so anytime she wants. But she doesn't want to convert, she wants to pose.