Doesn't Legal Realism have facets of both Natural Law and Positivism in it?

Yes and no. It has aspects apparently reminiscent of legal positivism and natural law, but it rejects both those positions. It rejects legal positivism because it minimises the importance of what is posited in precedents and statute books. And it rejects natural law because it makes no claim that morality is the governing criterion for laws. Morality is of course one factor upon which judges can make their decisions (just as it is one factor upon which parliaments can base their legislation) but it is by no means the only such factor.