An excellent question because "organic boycott" appears to have been "born" recently. My DDG search of the expression yielded seemingly nothing but results about this conflict. This bit from TIME appears to clarify:
Since the war in Gaza began, BDS has also endorsed new targets it did not initiate—like McDonald’s, Pizza Hut, and Burger King—calling them “organic boycott targets” because of the public support they have received after their brand franchises appeared to support Israel.
That's so cool!