Meet the well-funded advocacy network of liberal groups that orchestrated the successful ouster of the Benham Brothers from HGTV. Until last week, David and Jason Benham were set to host a new home-renovation show on the Home and Garden Television network, called “Flip It Forward.” But all that changed after an obscure website called Right Wing Watch drew negative attention to the Benham’s conservative views on abortion and gay marriage. The website vilified the hosts with the headline, “HGTV Picks Anti-Gay, Anti-Choice Extremist For New Reality TV Show.” The story shed light on how the hosts’ father, Flip Benham, is...